Update on my experience.

I had no problem checking in at JFK. The agent asked if I had a UK visa & I told him I was transiting on the basis of my US visa. No further questions were asked.

I landed in LHR & went for immigration. The officer asked me when my next flight was & I told him I had a booking for later that day as well as another one for the following day depending on his discretion to let me in. He said I was permitted to stay till midnight on the following day. So I went into the city, met up with some friends, stayed the night & left for CDG the next evening.