The phrase cucumber sandwiches on the lawn and its variants have been used to characterise traditional Englishness.

Cucumber sandwiches have indeed been served at garden tea parties—as illustrated by the following three passages from stories published in the first half of the 20^th century:

1-: From Chapters VI and VII of The Golden Hope, a novel by J. S. Fletcher, published in the Islington Daily Gazette and North London Tribune (London, England) of Friday 23^rd August 1912:

“Come, Mr. Workman, Miss Delomosne will be giving our guests some tea on the lawn—come and be introduced to her, and join in our English five o’clock.”
Laurence had no objection to this proposal, and he followed Sir Herbert across numerous rooms, and along various corridors, until they emerged upon a smooth lawn, gaily bordered with flowers. And there, chatting vivaciously with M. L’Abbé Bremond, he saw, presiding at a tea-table, the hawk-eyed lady with whom he had crossed from Ostend.
Brought face to face with two people who during the past two days had entered somewhat mysteriously into his life Laurence felt as if had fallen amongst old friends.
“But there is no need introduce me, Sir Herbert,” he said. “M. L’Abbé Bremond I already knew, and this lady […]. One always wants to see anyone whom one meets and is interested in—don’t you think so, M. L’Abbé?”
“Quite true—quite true, my friend,” responded M. Bremond. “And I am glad to see that you are one of those very rare young gentlemen who in this blasé age take an interest in their fellow-creatures. It is—yes, quite refreshing.”
Laurence, with a mouth full of cucumber sandwich, gave the ecclesiastic a stare of wonder.

2-: From Chapter III of The Years of Hate, a novel by Guy Thorne, published in the Todmorden Advertiser, and Hebden Bridge Newsletter (Todmorden, Yorkshire, England) of Friday 29^th June 1923—claret-cup designates a mixture of iced claret with lemonade and various flavouring ingredients:

It was late in July and the afternoon of the new rector’s garden party. […]
[…]
[…] To-day when the trim lawns were covered with happy people, when innumerable little tables for tea and claret-cup were set out under the trees and the string band discoursed popular music, the fine gardens made as gay and pleasing a picture as the eye could rest upon. […]
[…]
[…] The villagers […] were well catered for by a host who understood his guests. They might have had claret-cup, cucumber sandwiches and lobster mayonnaise […] but as there was a discreet tent where mild beer awaited those in search of it on this hot afternoon, the claret-cup was not unduly called upon, while lobster cream and prawn sandwiches were not regarded as luxuries by those who gained their livelihood by catching them.

3-: From Love If You Dare, by Dorothy Quentin, published in the Courier and Advertiser (Dundee, Angus, Scotland) of Monday 30^th December 1940:

Throughout the simple ceremony Jill and David were in an agony of shyness. It was so simple, so significant, somehow, as if they had been brought into spiritual contact for the first time. A contact that frightened Jill and exalted David.
They were both glad to get outside afterwards into the humdrum throb of chatter and laughter, to be absorbed in the crowd, to lose that mystical thread binding them together.
The Dales had invited about twenty of the villagers to a christening party at the farm, and, of course, the god-parents were the guests of honour. The party was a simple affair, a real country tea. Jill thought of the guests at Lilac Cottage nibbling cucumber sandwiches on the lawn, and smiled.

Paul Holt told the following story in The Tatler and Bystander (London, England) of Wednesday 14^th September 1949:

A cook-housekeeper I know has a brother who is a butler who is a snob. Whenever she visits him he tirelessly hints that while he serves the nobility her master and mistress are most patently untitled. It was in some triumph, therefore, that she set off the other day to see him, bearing in her handbag a snapshot which showed her handing cucumber sandwiches on the lawn to the Duke of Edinburgh, who was a member of a visiting cricket team.
Having the initiative, for her brother was deeply impressed, she prodded and prodded and finally disclosed her mass of manoeuvre. Staring out of the window she cried, “Who on earth are those people walking across the lawn?” The butler blenched. “His Lordship having donated this estate to the Government,” he answered icily—“. . . those people are the Public.”
“Oh, indeed?” replied his sister. “My Mr. Smith, now. He’s most particular who he has on his land.”
Her victory is complete and, I believe, final.

Peter Wilson, sports editor of the Daily Mirror (London, England), used the metaphor on two occasions about lawn tennis:

1-: In the account of the match between two English tennis players, Shirley Bloomer and Pat Ward, on the Centre Court at Wimbledon, published on Wednesday 26^th June 1957:

There was, even on this most famous court in the world, just the suggestion of the tinkle of tea-cups round the vicarage lawn.
And the feeling that the ball boys might stop throwing the balls to the players and start handing round cucumber sandwiches—cut very thin of course.

2-: In the account of a match between the U.S. tennis player Pancho Gonzales and the Australian tennis player Lew Hoad, published on Tuesday 8^th April 1958:

For years there was a widely held notion that there was something mildly effeminate about lawn tennis—a vague odour of cucumber sandwiches, China tea and the vicarage lawn.

From the column Rugby and Round About, published in The Coventry Evening Telegraph (Coventry, Warwickshire, England) of Thursday 8^th June 1961, the following expresses nostalgia for time past:

The garden party, as everywhere, is a delightfully popular pastime in Rugby—a pleasant throwback to more leisurely days when there was time to appreciate the subtleties of herbaceous borders, rolling lawns and delicate cucumber sandwiches.

Rex North told the following story in the column North stars, published in the Daily Mirror (London, England) of Friday 7^th July 1961—Peter Sellers (1925-1980) was an English comic actor:

An afternoon in the sunshine on the lawns of Buckingham Palace yesterday at the Queen’s garden party. . .
[…]
Peter Sellers, heading a formidable show-business delegation, sported a vivid green tie—“To match the cucumber sandwiches,” he explained.

Doone Beal expressed nostalgia in The soft safari, published in The Tatler (London, England) of Wednesday 7^th February 1962:

Within a 100 miles of Nairobi there is a variety of pleasant, English-type hotels: the White Rhino as well as the Outspan, both at Nyeri, and the Brackenhurst, at Limuru, all with adjacent golf courses. At Limuru especially, the hydrangeas and the lawns, the cucumber sandwiches for tea, the conversation and the company, belong to a sublimated Sussex in this—to me—the saddest of all nostalgias.

The following is from an article about hats, by Susan Brett, published in The Coventry Evening Telegraph (Coventry, Warwickshire, England) of Thursday 28^th February 1963:

The very sight of a boater calls to mind pictures of trailing dresses on Edwardian lawns, frilly parasols and cucumber sandwiches . . . and, of course, punting on the river.

Jon Akass wrote the following about croquet in the Daily Herald (London, England) of Saturday 6^th June 1964:

Croquet is fixed forever in a Wonderland world of comic curates, crinolines and cucumber sandwiches. Nothing will shift it.

Published in The Sydney Morning Herald (Sydney, New South Wales, Australia) of Wednesday 22^nd February 1967, this advertisement explicitly uses the phrase to characterise traditional Englishness:

BUYING A BUSINESS?
Come to where the flavour is. Here, right here, in this Olde English style Restaurant cum tea shop. A rural setting of pastures green. Exclusive attractive, it smacks of Retired Colonels, Victorians and cucumber sandwiches served on the lawn. Small attract. Res. provided, its [sic] 80 mls. S.W. of Sydney. Price £3000.

The collocation occurs in this passage from A Strange Meeting, a short story by the British author William Sansom (1912-1976), published in The Listener (London: British Broadcasting Corporation) of 23^rd March 1967:

Love indeed called to mind a memory of a time when as a young man in just such a lane there had been a heavy rainstorm; and ahead of him he saw a woman without an umbrella, without even a coat, getting drenched through. He had walked faster to overtake her and offered the shelter of his own umbrella, with, it always seemed to him, the kind of smile and soft tone of voice you would connect with cucumber sandwiches and a vicarage lawn. Her answer? She took to her heels and ran like blue hell.

In Thoroughly Wholesome Julie, a portrait of the English actress and singer Julie Andrews (Julia Elizabeth Wells – born 1935), published in the Los Angeles Times (Los Angeles, California, U.S.A.) of Sunday 15^th October 1967, Jane Wilson associated the phrase with jolly hockey stick(s), which denotes a woman or girl having a boisterous or hearty manner regarded as characteristic of a type of upper-class English public-schoolgirl:

She lacks the necessary decadence of the day. She is branded with the Good Housekeeping Seal, and she remains wholesome.
She winces at the word. “No I don’t want to be thought of as wholesome! It does rather lack any suggestion of mystery.” But Julie’s wholesomeness is in itself a dark mystery. She comes on like an English country dollie—all cucumber-sandwiches-on-the-lawn, dogs, tennis parties and membership in the local dramatic society. How did she get like that? Her childhood and teens, as she tells it, sound abnormal, unhealthy. Then there is always that odd little admission—“I’d be terrified of what I’d reveal if I ever really let go!” Her English Rose jolly-hockey-stick manner is being supplanted now, when she remembers, with a faintly imperious style more suited to the “last of the really great dames.”

And, in Young World: Fashion for boys and girls, published in The Sun-Herald (Sydney, New South Wales, Australia) of Sunday 12^th May 1968, Dale Plummer associated the phrase not only with jolly hockey stick(s), but also with a stiff upper lip, which is now understood as referring to what is believed to be a quintessentially British trait, the repression of emotion:

Cucumber sandwiches and all that jazz . . .
Jolly hockey stick, cucumber sandwiches on the croquet lawn with the vicar and all things British! Here’s your opportunity to become a member of the “I’m backing Britain” brigade.
David Jones’ stores in various part of Australia are “going British” with a series of attractions designed to give you a taste of English life and atmosphere.
In the Sydney store it’s all happening tomorrow and for the next fortnight you can be all stiff upper lip under a nine-foot scale model of the statue of Eros, or a replica of the Big Ben Tower complete with clock and recorded chimes; view an exhibition of the works of famous English photographers or a huge working model of London airport.