Direct scheduled flights -Direct flights exist from both Heathrow and also Gatwick on an almost daily basis.
These are to Bourgas, Varna and Sofia only. (British Airways, Bulgaria Air, Thompson fly, Bolkan Holidays etc),
Wizz Air is a European low-cost airline with direct flights from Luton Airport to Sofia and Bourgas.

Charter flights can be convenient for many and whilst they do have advantages they also have disadvantages.
Summer Charters run from virtually all the main UK provincial airports such as Manchester, Birmingham, Newcastle and Glasgow as well as many many more.
They fly direct to Bourgas on the Southern Coastline or to Varna on the Northern Black Sea Coast.