Around 1960 in Britain "Have you a camera?" or "Do you have a camera?"

Interesting question. According to Ngrams, "Have you a" was more common than "Do you have a" in the past, but it has reversed over time. Here, in British English, the reversal was around 1980:

The same search for American English shows the reversal around 1940:

I'll supplement the NGram answers with some corpus data, which shows Have you + NP was in oral use in Great Britain. These samples come from the British National Corpus, which has both oral and print samples from the 1980s and 1990s. Searches and examples show that Have you + NP was still in use even at that time, though it may have been in decline compared to alternatives.

Search 1: "Have you a" - 50 results

• "Have you a smoke now?" "Oh yeah, I've got some." (PS01A, 1-6 Feb 1992)
• "Have you a dark grey? No?" "No. I have no grey." (PS1HH, 15-17 Apr 1992)
• "Ah well I got the bloody fright of my life once. When I was in seeing the (pause) the banker, and he said to me he said, have you, have you a will made? Says I, no." (Oral history project: interview)

Search 2: "Have you any" - 222 results

• "Thank you. Erm (pause) have you any (pause) do you sell fish fingers?" (PS1A9, 2-9 Apr 1992; note the mid-utterance shift, something I saw in one other result)
• "Have you any money?" (PS0MA, 14-16 Apr 1992)
• "Have you any idea how many books you might actually sell?" (Town council grants meeting, 21 Feb 1993)

Searches 3 & 4: "Do you have a" - 186 results; "Do you have any" - 178 results

• "Do you have a secret deal with Oxfam?" (PS05X, 31 May - 1 Jun 1991)
• "Do you have a blazer for school?" (PS1HH, 15-17 Apr 1992)
• "Do you have a black skirt?" "Only a short one." (PS52C, 1993)

Search 5 - "Have you got a" - 314 results

• "Have you got a ruler?" "Yes." (PS002, 13-16 Mar 1992)
• "Have you got a car? "No, I haven't." (PS029, 2-6 Dec 1991)
• "Edward. Have you got a smelly bum?" (PS1A9, 2-9 Apr 1992)

Basically, the have you + NP construction continued to be in usage through the early 1990s, though the usages with do or the usage with got are widespread. I see in a couple of cases a tendency to self-correct to a do-construction ("Have you any (pause) do you sell fish fingers?") or to respond in a different form ("Have you a smoke now?" "Oh yeah, I've got some."). Over the past thirty years, it's quite likely the have you + NP usage has almost entirely aged out of the population.

Bonus: to the exact question of whether this would have also been used in the 1960s, yes, it would have. The Hansard Corpus for British Parliament provides a couple of examples of spoken use from the decade:

I wanted to allow the inspector to seize a display ticket which was actually on the goods to be seen, not to say to the seller: " Have you a display ticket for this? " and then take it: (Faringdon, Weights and Measures Bill, House of Lords, 6 May 1963)

When he was asked by the interviewer: " Have you a partner? ", he said, " Yes " (Thomas Jones, Welsh Language Bill, House of Lords, 15 June 1967)

These Ngram comparisons may help:

with "a"
with "any"

Around 1960, when it was my job to collect eggs from the hen-house, a visiting grandmother would often ask, "Have we any eggs?" If someone sneezed she would ask, "Have you a cold?" or "Has he a chill?"

(Btw, "Baa Baa Black Sheep" would need a 5/8 bar to accommodate 'Do you have any'.)

I was born in England in 1960, went to a normal state primary school and then in September 1971 to a direct grant school (yes, they still existed). I well remember our first Latin teacher spending the first six weeks teaching us English grammar, on the grounds that we could not hope to learn Latin, until we understood at least some of the grammar of our own language. He covered also the way words change over time: got as a past participle was compared to forgotten and ill-gotten (and also with gotten in North America). So certainly as of September 1971 "Have you got" was idiomatic in British English.

As anecdotal evidence in support of this, still in 1974 the Two Ronnies could make a sketch "Swedish Made Simple", with FUNEX (can be found on YouTube). This only works if "Have you any" was reasonably idiomatic at the time in Britain.

As a side note, though, I would point out that the form "Do you have a ..." is regularly used with the implied meaning "now, on your person". For example someone wanting to light a cigarette might well ask, "Do you have a lighter?". Here they would not be asking, whether you own a lighter, but whether you have one on you at that specific moment. As far as I can recall, this usage goes back to my childhood: "Do you have a ball?" - so that we can play football (soccer) now.

"Have you a camera?" is archaic, but certain English dialects, particularly in the North, like Yorkshire, have kept more archaic features and they were more distinct around 1960.

Using do as in "Do you have a camera?" is called a "Periphrastic Do" and was "invented" around 1500 in the South of England. Before that, English, as a Germanic language, was like modern German, with no need of a DO and reverse subject-verb order. E.g. "Sprechen sie Deutsch?" -> "Speakest thou English?" -> "Do you speak English?"

Today it's only used(outside aforementioned dialects) to deliberately convey an "old-timey" feel to some character. E.g. Aragorn, in the famous LOTR scene, when speaking with the (really old) dead, does not say: "What do you say(to my offer)?", he says:

Even though he speaks "modern" throughout the movie.