I hadn't really thought of that Sonny and Cher song ("I Got You Babe", since he sings "I've Got You"..)
I had always thought he was mimicing the same jaunty cadence of the classic Cole Porter 'I've Got You (Under my Skin')- which made sense to me at the time,
since some of his following lines are "I am you - prepared to do anything...", plus Mark Gatiss loves musicals.
Of course that 'Parachute' song has perfect lyrics for this, and the original Ingrid Michaelson version was probably popular around when this was being filmed...
Or it's just mockery.
Who knows what goes on in that funny head of his.