The leading actor nomination, for Burton and Taylor, was paired with a nomination for co-star Helena Bonham Carter for her portrayal of Elizabeth Taylor.
But both will face tough competition, with Broadchurch star Olivia Colman also up for leading actress, and Jamie Dornan among those nominated in the actor category for The Fall.
Sarah Lancashire and Nicola Walker are both nominated in the supporting actress category for Last Tango In Halifax.
BBC drama The Great Train Robbery, filmed across Yorkshire last year, is up for best mini series. Scenes were filmed in Leeds, Bradford, Shipley and Goole, and the Keighley and Worth Valley Railway was used as Sears Crossing, where the actual robbery took place.
Educating Yorkshire, filmed at Thornhill Community Academy in Dewsbury, is nominated for best factual series. It will also face stiff competition from the likes of Gogglebox, Breaking Bad, Broadchurch, and Doctor Who: The Day Of The Doctor, in the Radio Times Audience Award, which is voted for by the public.
Bradford magician Steven Frayne, better known as Dynamo, will go against the likes of Ant And Dec’s Saturday Night Takeaway and Strictly Come Dancing in the Entertainment category for Dynamo: Magician Impossible.
The Bafta television awards will take place on May 18.