On the return leg, at JFK, there is no need to go to a desk to for visa check if you OCLI and printing your BP with hand luggage only. This is a LHR T5 requirement only. Does not even apply to BA flights at LHR T3 or LHR T4.

At JFK T7 which is the BA terminal, make sure you go to far side of the building if arriving by car/taxi or the left side which is where all the CW and First check in desk are. Walk past the CW check in desks and there is a separate Fast Track lane for CW and F pax opposite the F desk check-in. It true feels like a "lane" a it is a tunnel-like corridor where there are two security machines and never any queue. The main security machines for WT and WT+ pax are on the other side of the building.

If you are on an evening return flight, you will have to eat at the lounge if you are flying CW since this would likely be a sleeper service.