It would help if we knew where you were starting out from ;-)
(There's probably not much point in checking whether there are any flights from, say, Cardiff if you live in Aberdeen!)
As a starting point, I'll provide you with a list of all airlines flying from London to Cyprus:
London City Airport: No services.
Luton Airport: No services to Larnaca. ThomsonFly and Libra Holidays operate to Paphos.
Stansted Airport: The only services (both to Larnaca and Paphos) are with Cyprus Airways.
Heathrow Airport: There are no flights to Paphos. Cyprus Airways and BA operate to Larnaca.
Gatwick Airport: Eurocypria (which is part of the Cyprus Airways group), Excel, First Choice, MyTravel, Thomas Cook and ThomsonFly all operate to both Larnaca and Paphos. GB Airways (which is a division of BA) and FlyJet also operate to Paphos.
If you're looking for reasonably priced 'quality' airlines from among that lot (apart from Cyprus Airways), check out GB Airways (which uses BA liveried aircraft and BA staff, but is frequently much cheaper than BA-badged services) and Eurocypria (which seems to be doing the same type of thing for Cyprus Airways). FlyJet might also be worth checking out. (Their flights can only be booked through a travel agent, not online. They seem to be 'take the middle ground in the way they operate i.e. seats are normally allocated omn a'first come - first served' basis but an in-flight meal is included in the fare).
Now that I've typed all of that out, you'll probably tell me that you really do live in Aberdeen ;-)
Chris