Yes, you can be on a through ticket even with different and competing airlines. The advantage is the ability for BA to check your bags through to JFK at GLA, and at JFK, you can check your bags through to GLA. The two carriers likely do have an agreement to do this, but I wouldn't suspect that you'll be able to get a boarding pass for VS from BA or vice versa. If you cannot, the transfer desk area at LHR should be able to provide one. You shouldn't have to leave the secure area.
should he??