This link shows every airline operating into Dalaman from the UK, so at least you'll know where to start looking for cheap(-ish) flights:
http://www.atmairport...ompany_en.php?ulke=UK
Well, it SHOULD show all airlines but it doesn't seem to be particularly up to date because several of those companies have gone bust. You might find Wikipedia to be more accurate:
http://en.wikipedia.org/wiki/Dalaman_Airport
Thomas Cook has some fairly cheap outbound flights towards the end of August (typically £84.99 including tax) but return flights are generally dearer (around £200 including tax).
Similarly Monarch can fly you TO Dalaman (from Birmingham) for under £80 including taxes but coming back FROM Dalaman will cost you around £200.
When considering your options, remember that it might be best to fly out with one airline and back with another. Also, if you use public transport, rather than driving to the airport, it often makes sense to fly out from one UK airport and come back via a different one.
Chris