The phrase interview without coffee is a British-Army euphemism for a severe reprimand by a senior officer. It has come to also denote, by extension, any ‘dressing-down’.

These are, in chronological order, the earliest occurrences of the phrase interview without coffee that I have found:

1-: From Greater communication urged to fight drugs, by John Goodbody, published in The Times (London, England) of Monday 2^nd April 1990—the British pentathlon team had won bronze at the 1988 Summer Olympics in Seoul, South Korea:

Dominic Mahony, a member of the team which was third in the modern pentathlon, told the first British Olympic Association (BOA) competitors’ conference yesterday that individuals who produce irregular urine samples should be interviewed informally by a representative of the Medical Commission of the International Olympic Committee (IOC) before having to attend a formal meeting of the Commission.
[…]
Mahony said that the final interview by the IOC Medical Commission “was one of the most unpleasant, intimidating experiences of my life. After two carefree days, with a medal burning a hole in my pocket, it was an interview without coffee. It was not a pleasant experience.”

2-: From Reasons in Writing: A Commando’s View of the Falklands War (Barnsley (South Yorkshire): Leo Cooper, 1993), an account of the 1982 Falklands War by the Royal-Marine officer Ewen Southby-Tailyour:

I was summoned, without warning, to call on the Chief of Staff to the Commander-in-Chief. I had called on the Admiral before but on this second occasion I became suspicious when ordered to arrive in full Lovat uniform—the usual sign that, as some joker put it, it would be an interview without coffee!

3-: From Bosnia Warriors: Living on the Front Line (London: Robert Hale Limited, 1998), an account of United-Nations operations in Bosnia, by the British-Army infantry officer Vaughan Kent-Payne:

When we returned, I learned that one of the subbies had been summoned for an interview without coffee with James Myles.
[…]
I decided to take it on the chin and say nothing. Roy had also been invited for an interview without coffee and had the misfortune to go in first.

4-: From Troops face an unacceptable level of risk, by Robert Fox, Defence Correspondent, published in the Evening Standard (London, England) of Monday 19^th January 2004—the Labour-Party politician Geoffrey Hoon (born 1953) was then the Secretary of State for Defence:

The meeting between Geoff Hoon and Samantha, the widow of Sergeant Steve Roberts, shot after he had handed back his body armour in Iraq, will have been something of an interview without coffee—military jargon for a commander’s dressing-down of a subordinate. Samantha Roberts is well able to stand her ground, and now she is joined by another Iraq widow, Tracey Pritchard, whose husband Corporal Dewi Pritchard was shot dead in his unprotected car last August, several weeks after his unit had asked for armour-plated vehicles.

5-: From Putting this lady’s amorous career to bed won’t be easy, by Geoffrey Wheatcroft, published in the Sunday Independent (Dublin, County Dublin, Ireland) of Sunday 26^th December 2004:
—The Group (1963) is a novel by the U.S. author Mary McCarthy (1912-1989), describing the lives of eight female friends after their graduation from Vassar College, in Poughkeepsie, New York. Kimberly Quinn (born 1961), who graduated from Vassar College, is a U.S. journalist; she had an affair with David Blunkett (born 1947), who resigned as Home Secretary on 15^th December 2004. Simon Hoggart (1946-2014) was a British journalist:

Not since the ladies immortalised by Mary McCarthy in her saucy novel The Group has any Vassar girl done so much for her sex, or just for sex, and chattering London was agog even before Simon Hoggart, one more Guardian journalist, was outed as yet another of Kimberly’s squeezes (by whom? It has been suggested that the Special Branch would have been watching Kimberly on Blunkett’s behalf and keeping him informed of any other frolics of hers).
Since it’s the festive season, and since Simon is one of the most popular figures in Fleet Street or Westminster, whom I’ve known for very many years as a decent skin, I shall treat him gently. One might possibly wonder what on earth he thought he was up to, but then I daresay that point has already been made by his charming wife Alyson in the course of what the British Army calls an interview without coffee.