Have you tried http://www.ba.com?

Viv

Try http://www.priceright.net
I book a lot of flights to Cyprus and normally find them the cheapest. The flights are with Excel from Birmingham on a fri night and Eurocypria from East Midlands on a sat night. Prices include the meal.

Also try First Choice they fly from Birmingham and East Midlands (both Sunday flights) and normally reasonably priced. You won't get one to Larnaca from Cov (not to my knowledge anyway let me know if I'm wrong?)

Flythomascook.com fly from Birmingham they're hit and miss I find, you will either get a really good deal or else they'll be very expensive!

Thomson fly from Birmingham and East Mids but normally expensive for flight only.

If you're not necessarily looking for the cheapest deal, also try BA or Cyprus Airways. Cyprus Airways def fly to Birmingham and very good airline.