Fallout 3 will give you a better idea of what life will be like in a year or two as Vegas was protected from the nuclear war to some extent by anti-ballistic lasers (or missiles, I can't remember tbh) so only a few nukes exploded in the area around Vegas. I doubt Britain has any anti-missile capability so we'd be more like Washington D.C. which got the full force of the Nuclear war
Anti-missile capability is smoke and mirrors; there is no such thing as an effective defense against multiple reentry warheads, so rest easy knowing that Britain would be no more or less vaporized than any other population centre.