As Norman states, there are summer flights from many UK airports to Larnaca. However, some people buy timeshares in Cyprus, only to find that the availability of flights outside of the main summer period is very limited (and cheap fares are even harder to find).
I think Norman might be wrong about Norwich. Their website only mentions flights to Paphos. From most other airports, there are plenty of charter flights but not many scheduled services. For example, the only scheduled operator ex Manchester is Cyprus Airways. However, there are charter flights with Eurocypria (which is the budget arm of Cyprus Airways), Excel, FlyJet, Futura, MyTravel, Thomas Cook and ThomsonFly.
It would take most of the evening to compile a detailed list of all available services from every airport in the UK. If you want more detailed information for airports close to where you live, please post again, stating your location.
Chris