I think BA’s the only company flying LHR-NCL, they operate 6 flights a day, with equipment used being the 737/757, A319/A320. They’re also QF codeshare flights, if you’re booking downunder. Flight time is just over an hour.
By road, it’d be a pain in the arse, as the Motorways are invariably clogged up around public holidays, driving to Newcastle’d probably be around 6-7 hours drive.
If you want to take the train, it’d be GNER from Kings Cross, http://www.gner.co.uk taking about 3 hours.