I have been booking tickets for years. Expedia.co.uk is good. it lets you compare prices for a given date with several airlines. I would play around with the dates. this way you have a chance to strike lucky and get an underbooked flight which may mean - cheaper.

if you find a suitable flight with Qatar Airways then it may make sense to buy direct with them here. However due do big Xchange rate variations sometimes it is cheaper to buy in pounds, because the price you get on expedia doesnt reflect the xchange rate variation yet.

another thing is that some flights are very cheap from Dubai. you might want to investigate this. however this journey is less smooth.

good luck!