The flight to Las Vegas is rather longer than that, Slinkycat. Virgin Atlantic quote 10 hours 45 minutes outbound from Gatwick to McCarran International, with 9 hours 50 minutes for the return flight.
As Slinkycat states though, any flight to the USA is going to take well over 4 hours. The shortest flight would probably be to New York. Virgin Atlantic quote Heathrow to JFK as 7 hours 40 minutes outbound and 7 hours back. However you'd still be over 2500 miles (by road or rail) from Las Vegas. That's the same distance as London is from Baku in Azerbaijan!
There's no real way of breaking the journey up. It would take many days by bus. US inter-city rail services are almost non-existent. (Where we'd expect to see a service between two particular cities every half hour, the USA often has only 2 or 3 trains per week. Further, the nearest stations to Las Vegas, in Needles and Kingman, are both around 100 miles away)
Las Vegas is in the middle of thousands of square miles of desert. There is no easy way of getting there other than by air. Your only sensible option (other than getting completely boozed up on the flight) is to invest in a 'Fear of Flying' course, such as the one run by Virgin Atlantic:
http://www.flyingwithoutfear.info/
Chris