From what I know about the case, and I've only read a book or two on it and quite long ago, the friend that Turing took home later broke in to his house or something to that effect. Turing reported to the police and in the process of the investigation the whole thing spilled out.
So, even if it wasn't the first time he acted that way it doesn't really matter because there is 0 proof that Turing was 'blackmailable' because of his sexuality.
The whole situation appears to have been an attempted blackmail, Turing meets a teenager at the cinema in the week and invites him back to his for sex, they meet that weekend (with another person IIRC) and have sexual relations and the youth takes some of Turings possessions (money can be a possession, Secret government docs can be too(!), something was taken) presumably under the belief that Turing wouldn't report it due to their relationship - approximating blackmail at least. Turing reports the larceny (theft of sorts) to the Police, they ask him what the youth was doing there and Turing told them. Resulting in Turing and the youth both being arrested.
I'd warrant there is no record anywhere to show this wasn't an attempt at blackmail as part of espionage activities - but you're right he turned out not to be blackmail-able in this instance as he went to the police. But one does not know whether he was in a trap and realised it or not in a trap at all.
The MI6 file on this would make an interesting read I'm sure.
From what I know about the case, and I've only read a book or two on it and quite long ago, the friend that Turing took home later broke in to his house or something to that effect. Turing reported to the police and in the process of the investigation the whole thing spilled out.
So, even if it wasn't the first time he acted that way it doesn't really matter because there is 0 proof that Turing was 'blackmailable' because of his sexuality.