Just thought of another option. I note what hellsbrink says about Jet2.com's punctuality, so that needs to be considered when making a choice. But they also fly Newcastle-Prague three times a week, I think; you could stop there or change en route to and from Budapest. There are around five flights a day between PRG and BUD, mainly on Czech Airlines ATR-42s or -72s, and Malev Dash 8 Q400s.