I would stick with CW to LHR, pref on a 747.
Primarily because the UD is lovely, the Arrivals facilties at LHR are far superior, and you are not in a special rush to get into the West End.
The direct, non-stop JFK-LCY would win for speed to the West End, though, as almost guarantees no holding and baggage collection is super-fast.
The ideal is to take a day flight JFK (or EWR)-LHR, and although you lose the Arrivals lounge facility if using these services as you get in too late, you probably wouldn't need them anyway. I think those are both 777 services.
But, having said that, if you haven't tried the CWLCY service it might still be fun to do so..even though the LCY-JFK leg with the Shannon stopover is the more "interesting" leg to fly from an FT perspective