Yup, you can. We booked ours directly with BA, a little more expensive for the flights, but you can get cheap accommodation, so you can do it that way. Also, whizz air is pretty cheap, i am not sure if they fly to Sofia though. Hope that helps
You can get scheduled flights to Sofia but generally more expensive. As the others say Balkan Air is probably your best bet. Not up to BA or Virgin standards but acceptable. In flight catering is shabby but edible. Drinks usually no problem. Basic but workmanlike...typical Bulgarian. Watch out for flight timings though. Can be all over the shop!
in order of cheapest first - (unless you get an unusual bargain)
flythomascook.com - manchester to sofia
wizz air fly from luton to sofia and are comparable to easy jet standards
Bulgarian Air are cheap and cheerfull - no problems
BA - bit better standards but more expensive
try all the web sites and you should get all the info you need