Its star Sandra Bullock is up for best actress, while Alfonso Cuaron is nominated for best director.
Steve McQueen’s 12 Years a Slave had 10 nods, with five in the main categories including best film, best director and best actor for Chiwetel Ejiofor.
Michael Fassbender and Lupita Nyong’o also landed supporting nominations.
American Hustle equalled 12 Years a Slave’s tally, with nominations in all the acting categories for its stars Amy Adams, Christian Bale, Bradley Cooper and Jennifer Lawrence.
The 1970s drama, about two con artists who get entangled with the FBI, is also up for best film, with David O Russell nominated for best director and original screenplay.
Ejiofor, who was previously nominated for Bafta’s Rising Star award in 2006, told the BBC working on 12 Years a Slave was “one of the greatest experiences I’ve had as an actor”.
“To be received this way by Bafta is a really phenomenal moment,” he added.
Ejiofor will compete for his award against Bale, Tom Hanks for Captain Phillips, Bruce Dern for Nebraska and Leonardo DiCaprio for The Wolf of Wall Street.
The best actress category will see Bullock challenge Adams, Cate Blanchett for Blue Jasmine, Emma Thompson for Saving Mr Banks and Dame Judi Dench for Philomena.
The nominations saw Dame Judi set a Bafta record, with her 15th acting nomination.
That puts her one ahead of Meryl Streep, who was overlooked in the best actress category for August: Osage County.
“I’m very proud to be associated with this film and I thank Bafta voters for the nomination. I’m honoured and thrilled to be in such fine company,” Dame Judi said.
Other movies competing for best film include Captain Phillips and Philomena, while the latter is also nominated for best British film alongside Mandela: Long Walk to Freedom, Saving Mr Banks, The Selfish Giant and Rush.
Gravity, Saving Mr Banks and Rush all qualified for the British film category because they were either filmed in the UK, utilised British effects companies or employed other British talent, from writers to producers.
The rules are set out by the , which determines which films are eligible for UK tax relief.
Actress Helen McCrory, who announced the nominations, told the BBC it was important for Bafta to recognise British films separately.
“I think it’s important we let the world know what we’re doing here,” she said.
“We might have American actors in those leads, but this is British money, this is British craftsmanship and this is British investment. We should be incredibly proud and celebrate that.”
She also praised Ejiofor, calling him a “superb actor”.
“There’s a reason people rise within their professions, it’s not just talent and Chiwetel has the whole package – he’s intelligent, he’s eloquent and he’s talented.”
The best director category mirrored that of the Directors Guild of America – which announced its film nominations on Tuesday. Both bodies shortlisted McQueen, Cuaron and Russell alongside Paul Greengrass for Captain Phillips and Martin Scorsese for The Wolf of Wall Street.
BBC film critic Mark Kermode said although Gravity leads the nominations, his money was on 12 Years a Slave winning best film.
“It’s an extraordinary film… it is very, very powerful,” he said. “A wonderful leading performance from Chiwetel Ejiofor, who is absolutely fantastic in that central role.
“It’s one of those films – it has momentum, it has public support and critical support. I would be very surprised if it doesn’t come away from the awards ceremonies with several winners.”
Notable snubs in the acting categories included Robert Redford for sea drama All is Lost and Matthew McConaughey for Dallas Buyers Club – both of whom have been tipped for Oscar consideration this year.
British actor Idris Elba was also left off the shortlist for his portrayal of Nelson Mandela in Mandela: Long Walk to Freedom.
Monday saw Bafta announce the five young actors nominated for this year’s Rising Star award.
12 Years a Slave actress Nyong’o will compete against Blue is the Warmest Colour star Lea Seydoux and Sunshine on Leith’s George MacKay.
Will Poulter from We’re the Millers and Kill Your Darlings actor Dane DeHaan complete the list.
Winners will be announced at a ceremony at London’s Royal Opera House on 16 February.