I put my Virgin miles on Continental (who DO codeshare)-working on the basis I prefer AA for transatlantic but VS is my second choice (except for Vegas). Anything with NW DL or CO US domestic goes into the CO miles pot.
FF numbers can be segment related so you can claim AA miles for JFK LON and VS or CO (amongst others) for LON DEL.
If your ticket is refundable you could claim all your miles on Aadvantage if LON DEL is on BA-if rebooking is a viable option and you're not on a non refundable fare.