The phrase not waving but drowning is used of a person whose display of distress misleads others into underestimating this distress.

The following text illustrates this meaning; it is from Keith Waterhouse on Monday, published in the Daily Mirror (London, England) of Monday 13^th March 1972, by the British author and newspaper columnist Keith Waterhouse (1929-2009) ¹:

NOT WAVING . .
I expect there was a deep sigh of exasperation at the Home Office when Pauline Jones ² walked out of Askham Grange prison. The girl just won’t keep quiet, will she?
I am no psychiatrist but it seems obvious that everything she has done so far—the stealing of the baby, the wrist-slashing in Holloway, and now her abortive escape—has been a cry for help.
Now that Pauline is behind bars again, will Mr. Maudling’s advisers go on insisting that she does not need any specific psychiatric treatment? It is clear that she is a weak, self-dramatising, mixed-up young woman. But is that to be the end of her?
She is not just drawing attention to herself. To borrow some poignant words from the poet Stevie Smith, she is not waving but drowning.

¹ Keith Waterhouse coined red masthead, precursor of the British journalistic term red top.—Cf. also ‘since Pontius was a pilot’: meaning and origin.

² In October 1971, at Essex Assizes, Mr Justice O’Connor sentenced Pauline Jones, then 23 years old, to three years in Holloway prison. She had abducted a five-month-old girl called Denise Weller from a pram outside a chemist’s shop in Harlow, and had managed to hide both herself and the child for five weeks, during which time Denise had been mothered faultlessly. Pauline had done this desperate thing after suffering for several years of tumultuous grief, including the death of her much-loved mother, a disastrous second marriage by her father, desertion by a boyfriend, and a miscarriage. She was still suffering from the mental and emotional turmoil which so commonly follows childbirth and abortion when she took Denise.—Source: A groundling’s notebook: Judgement daze, by Donald Gould, published in the New Scientist (London, England) of Thursday 26^th July 1973.

As Keith Waterhouse remarked, the English poet and novelist Stevie Smith (Florence Margaret Smith – 1902-1971) originated the phrase, in Not Waving but Drowning, a poem in which a man’s plea for help is mistaken for a display of cheeriness.

It is often said that this poem was first published in Not Waving but Drowning: Poems (London: André Deutsch, 1957), but I have discovered that The Observer (London, England) had already published it, as follows, on Sunday 29^th August 1954:

Not Waving But Drowning

Nobody heard him, the dead man,
But still he lay moaning,
I was much further out than you thought
And not waving but drowning.

Poor chap, he always loved larking
And now he’s dead,
It must have been too cold for him his heart gave way,
They said.

Oh no no no, it was too cold always,
(Still the dead one lay moaning)
I was much too far out all my life
And not waving but drowning.

The first two occurrences that I have found of not waving but drowning used as a phrase:
– date from 1957;
– are from reviews of Not Waving but Drowning: Poems (London: André Deutsch, 1957);
– characterise Stevie Smith as a poet who is apparently light-hearted but in reality sombre.

1-: The first of these occurrences is from the review by Robin Skelton, published in the Manchester Guardian (Manchester, Lancashire, England) of Friday 4^th October 1957:

The gestures are often gay and the bathetic lapses funny, and the wide range of subject matter—from Fafnir the dragon to the dog Jumbo, from a version of Catullus to a poem upon “God the Eater”—has an endearingly haphazard quality. But Miss Smith is “not waving, but drowning”: her jokes are bitter, her parables disturbing, her pathos convincing.

2-: The second of these occurrences is from the review by Muriel Spark ³, published in The Observer (London, England) of Sunday 3^rd November 1957:

In the course of her work Miss Smith has created a poetic persona which she presents as a fantastic, somewhat blighted, observant and irrepressible soul, not so cheerful as you think, and “not waving but drowning.”

³ Muriel Spark (née Camberg – 1918-2006) was a Scottish novelist, short-story writer, poet and essayist.—Cf. also notes on ‘all fur coats and no knickers’.

The earliest occurrence that I have found of the phrase not waving but drowning used without explicit reference to Stevie Smith is from the review by Elizabeth Young of Les Pavillons: French Pavilions of the Eighteenth Century (London: Hamish Hamilton, 1962), by Cyril Connolly and Jerome Zerbe—review published in The Guardian (Manchester, Lancashire, England) of Friday 30^th November 1962:

“Not waving but drowning”: here are the bolt-holes of a politically castrated élite; houses small, by eighteenth-century standards, and charmingly civilised. Some are architectural fantasies; but each is an inhabitable dream to escape to from the nightmare of Versailles. A dream moreover of universal simplicity: a place for eating and drinking in peace, for talking sociably, and for making love. Ever for horse-play. Not for high thinking not for anything beyond the immediate relief of grinding tedium.

The phrase then occurs in Back on the Vietnam escalator, published in The Guardian (Manchester, Lancashire, England) of Tuesday 14^th February 1967:

President Johnson ⁴ has claimed for nearly two years to be listening for the slightest “signal” from Hanoi of its willingness to talk. In the past month these signals have been coming over loud and clear. […]
[…]
The Defence Department in Washington announced that “combat operations against military targets in North Vietnam” had been resumed. […] The more vigorously President Ho Chi Minh ⁵ signals, the greater will be the temptation to those who are running it in Washington and Saigon to carry on with more of what, in their view, has caused him to signal. They will assume he is “not waving but drowning.”

⁴ The U.S. Democratic statesman Lyndon Baines Johnson (1908-1973) was the 36^th President of the USA from 1963 to 1969.
⁵ The Vietnamese Communist statesman Ho Chi Minh (Nguyen That Thanh – 1890–1969) was the President of North Vietnam from 1954 to 1969.

A television programme first broadcast on BBC 2 on Wednesday 30^th May 1973 was titled:

Homes and the Homeless. Part 8. “Not waving but drowning.”

There have been numerous variants of the phrase. For example, a radio programme broadcast on BBC Radio 4 on Sunday 23^rd June 1974 was titled:

Waving and Drowning: portrait of Stevie Smith, poet.

Sandra Bisp used another variant in Day ‘Lillie’ got a watering, published in the Evening Post (Reading, Berkshire, England) of Saturday 14^th July 1979:

We were gathered together for a day in the production life of Why Didn’t they Ask Evans? the Agatha Christie classic comedy thriller.
[…] It was all tremendous fun, we were assured, as the rain washed gravy waves around the steak and kidney pie on our plates at the steps of the mobile canteen.
[…]
Apres le deluge—and a dessert of wet gateau—we were told we could talk to the stars. A sudden sodden stampede started from a line of sash-cord behind which we watching, waving and drowning journalists had been corralled.

Yet another variant occurs in the Evening Post (Reading, Berkshire, England) of Saturday 1^st December 1979:

Albums
The Boomtown Rats seem caught in their own rat trap. The Fine Art Of Surfacing (Ensign) is more artifice than art, the Rats not so much treading water as going under, weighed down by their own self-conscious attitudes. This is a prime example of a band waving while drowning.