Lee’s Comedy Vehicle has been shortlisted for best comedy programme alongside Charlie Brooker’s 2011 Wipe, the Comic Strip revival The Hunt for Tony Blair and The Cricklewood Greats.
It is a surprise nomination for the latter programme, a relatively low-profile BBC Four mockumentary presented by Peter Capaldi, who created it with The Thick Of It writer Tony Roche.
Mrs Brown’s Boys is up for two Baftas: best sitcom and best male performance in a comedy programme for its star and creator Brendan O’Carroll
Also up for best sitcom are Fresh Meat, Friday Night Dinner and Rev; while facing O’Carroll in the acting category are Darren Boyd for Spy, Hugh Bonneville for Twenty Twelve and Tom Hollander for Rev.
Shortlisted for best female performance in a comedy are Jennifer Saunders for Absolutely Fabulous, Olivia Colman for Twenty Twelve, Ruth Jones for Stella and Tamsin Greig for Friday Night Dinner.
Hart is nominated for her straight acting role in the BBC One drama Call The Midwife, where she is up against dramatic dame Maggie Smith for Downton Abbey, Anna Chancellor for The Hour and Monica Dolan for the Fred West mini-series Appropriate Adult.
Michael McIntyre’s Christmas Comedy Roadshow, Harry Hill’s TV Burp , Celebrity Juice and Derren Brown: The Experiments are nominated for best Entertainment Programme.
Over all the categories, ITV1's Appropriate Adult leads the nominations with four, including best mini-series, leading actor for Dominic West and leading actress for Emily Watson.
BBC One series Sherlock and Channel 4 drama This Is England '88 both received three nominations each.
Holy Flying Circus, about Monty Python’s fight with religious leaders over Life of Brian, is nominated for best Single Drama.
The winners are announced on May 27.