I would start by looking at AA availability connecting through NY, or ORD. If you can find availability then transferring to AAdvantage is probably the best use of the points. Redemption rates and surcharges on AA are pretty decent. If no availability the. I would look at Avios availability, surcharges will be high as they generally route through LHR, but if your going to fly J, then it can still be worth it. I travel almost exclusively on RBc points and found decent ways to get to LON a few times last year. If your willing to go Hand baggage only or do another hop look at flying to AMS or DUB to reduce the surcharges.