AAAGH! NOT AGAIN! Why is it that people who ask about flights TO a certain place never tell us where they're starting FROM. (It's rather pointless if we suggest flights from, say, Aberdeen if you live near to Southampton!).
Here's a complete list of UK scheduled, direct services to Budapest:
From Heathrow: BA
From Gatwick: easyJet, Malév Hungarian
From Luton: easyJet, Wizz Air
From Bristol: Ryanair
From East Midlands: Ryanair
From Prestwick: Ryanair
From Manchester: Jet2
If you live within range of Luton, Wizz Air (which is a budget airline based in Hungary) might well have the cheapest fares:
http://wizzair.com/
Chris