The noun plus-fours denotes men’s baggy knickerbockers reaching below the knee, formerly worn for sports activities, especially golf—cf. footnote.

The British-English phrase plus-fours and no breakfast is used of a man who pretends to be well-off despite having little money.

The image is of a man of limited means who spends what he has on smart clothes, and therefore cannot afford any breakfast.

—Cf. also the British-English phrase kippers and curtains, which conveys a similar meaning.

Both the phrases kippers and curtains and plus-fours and no breakfast occurred in the column Wales Day by Day, published in the Western Mail (Cardiff, Glamorgan, Wales) of Wednesday 6^th March 1957:

When I was young “kippers and curtains” was always good for a laugh as a description of lower middle-class pretentiousness.
“Plus-fours and no breakfast” was another side-splitter.

The phrase plus-fours and no breakfast is particularly associated with the Welsh poet Dylan Marlais Thomas (1914-1953), who recalled his younger self as follows in his thirty-minute radio piece Return Journey, commissioned by the BBC and first broadcast on Sunday 15^th June 1947:
—as published in Quite Early One Morning: broadcasts by Dylan Thomas (London: J. M. Dent & Sons Ltd, 1954):

He’d be about seventeen or eighteen […] and above medium height. Above medium height for Wales, I mean, he’s five foot six and a half. Thick blubber lips; snub nose; curly mousebrown hair; one front tooth broken after playing a game called Cats and Dogs, in the Mermaid, Mumbles; speaks rather fancy; truculent; plausible; a bit of a shower-off; plus-fours and no breakfast, you know; used to have poems printed in the Herald of Wales; there was one about an open-air performance of Electra in Mrs Bertie Perkins’s garden in Sketty; lived up the Uplands; a  bombastic adolescent provincial Bohemian with a thick-knotted artist’s tie made out of his sister’s scarf, she never knew where it had gone, and a cricket-shirt dyed bottle-green; a gabbing, ambitious, mock-tough, pretentious young man; and mole-y, too.

The earliest occurrences of the phrase plus-fours and no breakfast that I have found are as follows, in chronological order:

1-: From Answers to Correspondents, published in the West Bridgford Times & Echo (Nottingham, Nottinghamshire, England) of Friday 13^th June 1930—unfortunately, this newspaper did not publish Arthur’s question:

Arthur (Carlton).—Never mind if they do call after you “Plus fours and no breakfast.” If you went out minus them, you would probably get no peace either.

2-: From The Country Column, published in the Fleetwood Chronicle (Fleetwood, Lancashire, England) of Friday 8^th November 1935:

Bits of Wit and Wisdom
Clever Sayings by Village People
By R. G. S.

Country people […] have quick wits […]. Drawing similes from everyday things, they are able to coin descriptive phrases which are extraordinarily vivid.
I shall never forget, for instance, hearing a rather pompous little man who was putting up for a local Council described by a farm labourer as “like a young throstle, all behind and crop.”
[…]
I have heard a young man who was noted for dressing rather above his means described tersely as “plus fours and no breakfast.”
Of a mean woman it is said, “She’d flay a flea for its hide and tallow.”

3-: From Plus-Fours and No Breakfast: A Belfast Story (Belfast: Quota Press, 1937), the title of a novel by the Irish author Ruddick Millar (1907-1952); the following review of this novel is from the Belfast News-Letter (Belfast, County Antrim, Northern Ireland) of Thursday 2^nd December 1937:

As the author modestly explains “This is not supposed to be a ‘literary work.’ It is a simple straightforward story of one aspect of Belfast life.” It might aptly be described as a novel in miniature; for into its ten chapters is crowded as much incident as has often done duty in a more ambitious volume. Events truly march quickly in this account of a crisis in the affairs of the Malburn family, whose business is threatened with disaster during a lean time in the linen industry. How its various members react when household economies are demanded is graphically told, and there are surprises for the reader. Tragedy is here; but it is the turning point which leads to happier things, and we leave the Malburns a united family looking forward to the future with quiet confidence.

4-: From Superiority Complex: North and South, by ‘T. T.’, published in The Manchester Guardian (Manchester, Lancashire, England) of Thursday 10^th March 1938:

It was refreshing for me to travel south with a party of Lancastrians from “up th’ valley” who lambasted the Southerner with lusty relish. They all of them had to live (for their sins) in the South, and they made naught of it. […]
[…]
It would seem from this that though the Southerner has more silver in his tongue the Northerner has him whacked in trencher drill. Furthermore, he refuses to don an opera-hat at the expense of his stomach. My party were extremely sarcastic about plus-fours and no breakfast. But they did grudgingly admit that the Northern climate was hard to live with.

5-: From Letter To The Forces: Snobbery In The Turnip Field!, published in the Derby Evening Telegraph (Derby, Derbyshire, England) of Friday 9^th July 1943:

Don’t you believe it! Social snobbery to-day is just as patent as in the days when “the best people” had brass on their gates but little in their pockets, the days of plus-fours and no breakfast.

Note: The noun plus-fours is said to have arisen among cloth-cutters working for the tailors who first made the garment, as a purely descriptive term, four additional inches of fabric being added to the length of ordinary knickerbockers to produce the characteristic overhang.

The earliest occurrences of the noun plus-fours that I have found indicate that this garment was originally worn by the Foot Guards; these early occurrences are  from The Tailor and Cutter (London, England):

– of Thursday 15^th March 1917:

The Foot Guards […] wear a distinctive style from other infantry units, viz., wider overalls, really trousers; breeches, service or plus-fours, really knickerbockers.

– of Thursday 22^nd March 1917:

“Plus-Fours” is the style of leg-wear worn by the officers of the Foot Guards. It is really a modified form of the old-fashioned Knickerbocker cut full and long, with waist-bands and pleats, or cuts, and 2-inch garter or knee-bands, laced. Londoners are familiar with the style as worn by the officers and men, viz., the fall-over appearance of the trousers.

However, the following from The Tailor and Cutter (London, England) of Thursday 12^th July 1917 indicates that the garment was also worn by upper-class civilians:

In Diagrams 1 and 2 we are reproducing a pattern of knickers by West-Ender. These are knickers or knickerbockers proper, long and loose. So many so-called knickers with their deep bands approximate to breeches. Of course, such are required by many customers, and what they want they must have; but here we see the full-blooded, genuine, unequivocal garment, with no nip-cheese shortening or parsimonious narrowing. This is the type that your aristocrat wears, pleated at the waist, creased down the fronts, with a deep overlap at knee. Tailors used to call them “plus-fours”, and Varsity men, in elegant and classical phraseology, termed them “rice-bags”. They are finished at the knee with a narrow garter and buckle.