Many times in US airports there is a Continental codeshare desk located near the Virgin desk; I usually go directly to the Virgin UC desk and they send me back if there are any problems. In London go directly to the Virgin UC check-in counters.
You do have access to Virgin Clubhouses (as well as Continental ones), but not their Arrivals lounge; Continental uses the Air Canada lounge, which is still very nice, in Heathrow and they have a Presidents Club (with showers apparently) in Gatwick.
I have never managed to get Virgin limo service ahead of time; but Continental supposedly has limo service.
You cannot claim FC miles/points and I doubt you can pre-book seats with Virgin.
I have seen people wearing shorts in Clubhouses before..
Online reservations systems generally list the type of plane that is normally used; I would avoid the A340s like a plague. The seats are not reconfigured and the cabin is really just not as nice.
Hope this helps -h