November, high season slowly kicking in, will start to get expensive around then.
Try Emirates directly. I went return from November to March for £550 return on special to Singapore and booked cheap flights into and back out of Phuket with Tiger Air/Air Asia/Jetstar.
Other popular destinations to fly to prior to Phuket are Bangkok, Malysia (KL), Hong Kong.
I did Singapore return direct with Singapore Air for SUPER DAMN cheap in 2010 (Less than £450) but have not seen a deal like that since, worth trying them directly also though.
Lot's of other airlines fly into surrounding areas from London but most have horrendous scheudles/stops/layovers that are not worth the small savings. EVA Air, Air Asia, Thai Air, KLM etc etc. Best way to gauge other airlines is with skyscanner.net, opodo.co.uk, kayak.com etc
My advice - For the little extra just fly with a premier carrier like Emirates, it's actually not that much more expensive, if at all. Baggage, food etc is all included and you get the luxury of decent Economy (inflight entertainment, Power at seats etc)