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)