No simple answer
Sorry, but I don't believe there is a simple answer to this. As has been said, Virgin fly to both New York and Las Vegas but you will have to find a different airline between the two. Now, that could all be done on one ticket issued by Virgin or you could buy a ticket London/New York then Las Vegas/London and a separate New York/Las Vegas ticket.
But then you get into the question of non stop versus connecting flights. I have often been surprised to find that a connecting flight over a US hub (e.g. a-b via X) can be cheaper than non stop. So, it could be cheaper to go on United New York/Denver/Las Vegas than on a non stop flight.
And, as someone else has pointed out, if London is not your departure point then it may make most sense to start from your local airport. In which case take a look at Continental. They fly from (from memory) Gatwick, Heathrow, Bristol, Birmingham, Manchester, Edinburgh and Glasgow [Newcastle?]) to Newark which is just over the river from Manhattan and many people consider it more convenient than JFK anyway. Then continue on Continental to Las Vegas and fly back again via Newark.
Personally, I tend to value non stop flights and find Heathrow a convenient (if not beautiful) departure point so I'd go for the Virgin option for trans atlantic. As for New York/Las Vegas try JetBlue (would have to be bought separately) and then the following could all be bought separately or as part of your transatlantic whoever you use for those flights: Continental, Delta, US Air, American.
Cheapest is a misnomer. In the end you have to make a decision. You'll never know whether a further search or waiting until tomorrow might have saved you something (but it could also cost you). Pick flights that make sense to you in terms of time and what you can afford.