I would suggest you look into the EU regulations that exist. EU Regulation (EC) 261/2004 exists and protects passengers from delayed/cancelled flights from EU airports.
Please look at:
www.auc.org.uk
They may be able to help since you were delayed by more than a day to get to your final destination, even if you had to stop along the way. At the end of the day it wasn't a new flight, that flight number originated from LHR within the EU and was mean't to be non-stop to JFK.
Suggest you look into legal advice too. That is unbelievable that you were stuck on that flight for so long, I feel so much empathy especially for the people stuck in Economy class!