I think BA have a number of 777s (5?) without the First cabin, only Club, WT+ and WT. Surely these would be more suitable for a "bucket 'n spade" route.
(Although why it's referred to as such is madness; surely there are enough high-rollers in the UK to warrant a LAS service in a premium capacity? Or maybe loaded London-ites prefer a slightly more....refined....destination?
)