The informal British-English phrase one over the eight means: one drink too many.

The earliest instance of this phrase that I have found is from The Surrey Mirror and County Post (Reigate, Surrey) of Friday 15^th August 1919:

“ONE OVER THE EIGHT.”—At the Reigate Bench, on Monday, Frederick Powell, of Providence-terrace, London-road, Reigate, was charged with being drunk and disorderly on Saturday night.—P.C. Kimber proved the case.—Prisoner told the Court that he met an old uncle and had one or two drinks. He added “I suppose I got one over the eight, and I suppose I became a little quarrelsome.”—Fined 5s.

The question of the origin of the phrase was raised very early; for example, the following is from The Sussex Express and South Eastern Advertiser (Lewes, Sussex) of Friday 9^th June 1922:

AMUSING CASE IN LEWES COURT.

A very amusing case came before the magistrates at the Lewes Police Court on Tuesday when a man named Thomas Richard Colley, of 39, Stonecross-lane, Newhaven, was summoned on a charge of being drunk and incapable.
– P. C. Barrow said he found the defendant lying in the street in a helpless state. He found he was drunk. Defendant said to him “I have had one over the eight; will you look after me and see me all right?” (Laughter.)
– The Mayor (Alderman C. Patrick)—What is the meaning of the term? Has it any special meaning?
– Witness—It is a great saying this last few years.
– The Chairman (Mr. F. B. Whitfeld)—Does the man mean one over eight pints?
– Witness—It is just a saying.
– The Mayor—It does not mean that that is his limit?
– Witness—I do not know. (Laughter.)
– Defendant—I cannot remember anything about it. It seems to be a bit stronger ale here than in London. (Laughter.)
– The Chairman (smiling)—The case is dismissed.

The Evening Telegraph and Post (Dundee, Scotland) of Thursday 22^nd November 1923 proposed the following origin:

Judge Crawford, of Edmonton County Court, who was mystified by the colloquialism, “one over the eight”—which means that a man has had too many drinks—and endeavoured to discover its origin, will be interested to know that Mr Charles Austin, the comedian, claims to be the inventor of the phrase.
Charles Austin put the words into the mouth of Lorna Pounds when they were appearing in “Rockets” at the Palladium, London, last year.

But this explanation cannot be true, since the phrase was in use before 1922.

On Tuesday 20^th October 1925, the same Dundee newspaper explained that the origin of the expression

has been debated many times recently, and many theories have been advanced—none of them very convincing and none of them generally accepted.

The traditional explanation of the expression rests solely on the following from Soldier and Sailor Words and Phrases (London, 1925), by Edward Fraser and John Gibbons:

One over the eight, one drink too many. Slightly intoxicated, the presumption being that an average “moderate” man can safely drink eight glasses of beer.

But this origin is improbable, because the phrase did not appear in military or naval contexts (it is more likely that soldiers and sailors adopted an existing expression), and because the reference to eight glasses of beer looks like a later rationalisation.

It is probable that there is no logical explanation, that the number eight is arbitrary and that the expression is simply a euphemism for having too much to drink, regardless of the actual number of drinks that have been consumed.

Two punning uses of the phrase one over the eight, from The Pall Mall Gazette (London):

– of Thursday 6^th October 1921:

“THOSE AFTER-EIGHT SINS.”

A barman was yesterday fined 20s. for selling an ounce of tobacco after eight o’clock. As the law stands now you may have one over the eight with impunity, but not a bit of baccy after the eight.

– of Wednesday 7^th December 1921:

THE DOUBLE NINTH.

“I only had one over the eight,” said a man charged at the South-Western Court with drunkenness.
“And what was the ninth?” inquired the magistrate.
“A double scotch,” was the reply.