You could also try Kuwait Airways. I'm pretty sure that they serve JFK with a 772. They make a stop in LHR and you can buy a ticket for just the JFK-LHR leg.
Royal Jordanian flies JFK to SNN and then to Amman, but I bet you could get a ticket to just SNN and then fly to London from SNN on another airline. The Royal Jordanian flight would be with an A310-300.
Another option would be to fly from EWR to Rome on Ethiopian Airlines and then catch a flight to London from Rome on another airline. That is all considering you can just book a flight from EWR to Rome on Ethiopian Airlines and not have to continue on to Addis Ababa (their flight is EWR-Rome-Addis Ababa). The aircraft from EWR to Rome is a 763.
You could also take Uzbekistan Airways from JFK to I think Birmingham, England. That, again is condering that you can fly just to Birmingham and not have to continue onto Taskent. You could then fly another airline from Birmingham to London. The only problem with taking Uzbekistan Airways is that they only have 3 flight per week to JFK and only one of them uses the routing, JFK-Birmingham-Taskent. The other two operate JFK-Kiev-Taskent and Kiev would put you a ways away from London.
I hope this helps and have a great trip!