So many different airlines and options where flights to New York from London are concerned.
Indirect options include Ukraine International via Kiev. Turkish Airlines via Istanbul. Aeroflot via Moscow. Aer Lingus via Dublin. TAP Air Portugal via Lisbon. WOW Airlines & Icelandair operate via Reykjavik (Keflavik Airport). Air Canada could be another option via Toronto. I see plenty of people coming in on these routes when I'm at work (Gatwick Airport) as they are generally cheaper than some on the non-stop flights operated by airlines mentioned below.
Non-stop options as others have mentioned include BA, Virgin, Delta, American Airlines, United Airlines (all from Heathrow). Norwegian Airlines (from Gatwick).
I've been to New York 3 times before (wife has been 6 times). It's a great city, but mega busy, and very noisy so try and avoid staying right on top of Times Square would be my advise. I hope the OP has a great time as the city IMO is well worth a visit
Cheers
Ben