Check on BarrheadTravel.co.uk as they have some good Vegas deals just now (depending on when you wanna go).
I went to Vegas in December but can't really help as on the way out we did GLA->LHR->LAX (spent time in LA 1st as we were going on a cruise in and out of LA) we then flew from LA to Vegas (it's only like an hour). On the way back it was LAS->SFO->LHR->GLA which to be honest was a bit of a pain as effectively we were going backwards to San Fran to come forward again!
We all also found the time difference going to LA alone a bit of a nightmare compared to places we'd been before (NY and Orlando) as it's a much bigger gap!
Oh we flew with United! BMI down to and back from London though was a through ticket.