I think it very much depends when you are going, when you are returning & how far ahead you are booking Fred.
To be honest I usually look on the web at the usual suspects to get some sort of idea of cost & then (as Lee suggests) go into one of the local travel agents.
Last time I went/came was September (I only stayed 3 weeks). I used @here then & ended up getting an EVA return. They were (that day

) the cheapest direct return' although there was only a couple of 1,000 baht between them & Thai. Other times I have booked Thai have been outrageously priced, but not that time.
A friend of mine went a couple of months before me & went Jet (India) with a stop over in Mumbai. He said it was OK, but, at that time was VERY, VERY cheap. When I checked them, before I went, they were actually more expensive than Eva.
The flights that stop in the Middle East can also be cheapest, but can also be very inconvenient about the half way delay & also the starting & arriving time in BKK/London.
I think best suggestion is a quick explore at EVA/Thai/Jet/Emirates etc. then a quick trip to the Travel Agent to see what they can do - if you see a very special price on line & take a copy of it to @here they will match it!!!