The Hollywood musical, out in the UK on Friday, is up for best film, while stars Ryan Gosling and Emma Stone are up for best actor and actress.
British actors Emily Blunt, Andrew Garfield and Hugh Grant are also in line for acting awards.
Philosophical sci-fi film Arrival and Tom Ford's dark drama Nocturnal Animals have nine nominations apiece.
Bafta nominations in full
Seven things we learned from the nominations
Grant 'very pleased'
Ken Loach's I, Daniel Blake is up for both the best film and best British film awards.
The welfare state drama receives an additional nod for its screenplay while Hayley Squires, who plays a single mother in the film, is up for best supporting actress.
"As if @BAFTA think it's a good idea to put me in the same room as Ryan Gosling," tweeted the London-born actress, adding that she was "very grateful for the recognition".
Labour leader Jeremy Corbyn welcomed I, Daniel Blake's five nominations, congratulating Loach - who is up for best director - and "everyone involved in the brilliant film".
Grant, who plays Florence Foster Jenkins' partner St Clair Bayfield in the film about the singer's life, said: "This is so kind of Bafta and I feel very pleased both for myself and for St Clair Bayfield, neither of us having been exactly awards season habitues."
The British actor's only previous Bafta nomination, and award, came in 1995 for his role in Four Weddings and a Funeral.
Arrival, La La Land and I, Daniel Blake are joined in the best film category by Manchester by the Sea and Moonlight.
Other titles in contention for the outstanding British film award include Harry Potter spin-off Fantastic Beasts and Where to Find Them, which has five nominations in all.
Meryl Streep joins Blunt and Stone in the leading actress category, where she is nominated for her role in Florence Foster Jenkins.
Her 15th Bafta nomination puts her on an equal footing with Dame Judi Dench, who previously held the record for the most Bafta film nominations.
The US actress made headlines at the Golden Globes on Sunday with a speech in which she criticised US President-elect Donald Trump.
Mr Trump responded by claiming the three-time Oscar-winner and two-time Bafta recipient was "overrated".
Amy Adams and Natalie Portman complete the best actress contenders list, having been nominated for Arrival and Jackie respectively.
Gosling and Hacksaw Ridge star Garfield compete with Casey Affleck, Jake Gyllenhaal and Viggo Mortensen for the best actor award.
The latter trio are respectively nominated for Manchester by the Sea, Nocturnal Animals and Captain Fantastic.
Grant, who appears with Streep in Florence Foster Jenkins, is joined in the supporting actor category by fellow Brits Aaron Taylor-Johnson and Dev Patel.
Taylor-Johnson is nominated for his Golden Globe-winning turn in Nocturnal Animals, while Slumdog Millionaire star Patel is shortlisted for Lion.
"This Bafta nomination today truly means so much to me" said Patel in a statement. "My family is literally freaking out right now!"
"It's always nice to feel love from your hometown," said Taylor-Johnson, adding he was "genuinely humbled" by the "fantastic honour".
"Can't wait to celebrate back in good ole Blighty!" continued the 26-year-old, who is married to the British artist formerly known as Sam Taylor-Wood.
British actress Naomie Harris is also shortlisted for the supporting actress award for her work in independent film Moonlight.
Viola Davis, Nicole Kidman and Michelle Williams receive nominations in that category as well for Fences, Lion and Manchester by the Sea.
La La Land was the big winner at last weekend's Golden Globes, receiving every one of the seven awards for which it was nominated.
Its director, Damien Chazelle, is Bafta-shortlisted in both the director and original screenplay categories.
Kenneth Lonergan and Tom Ford also receive dual director and screenplay nods for Manchester by the Sea and Nocturnal Animals respectively.
Arrival's Denis Villeneuve joins Chazelle, Ford, Loach and Lonergan in the best director category.
Loach's nomination comes 50 years on from the Bafta TV award he received in 1967 for Cathy Come Home.
The 80-year-old film-maker received the organisation's Michael Balcon Award in 1994 and a Bafta Fellowship in 2006.
The Disney studio dominates the animated film category, scoring three of the four nominations with Finding Dory, Moana and Zootropolis.
Kubo and the Two Strings is the only nominee not to have been made by the so-called "House of Mouse" and its subsidiary Pixar.
Zootropolis co-director Rich Moore tweeted his thanks for his film's nomination, adding: "We will see you in London!"
Kubo director Travis Knight, meanwhile, said he was "thrilled and thankful" to be recognised for a film he said had been "a wholehearted labour of love".
Others to have tweeted reactions to the nominations include actor Russell Tovey, who said it was "huge" that his drama The Pass was shortlisted.
The Pass, in which Tovey plays a closeted gay footballer, receives a nomination in the outstanding debut by a British writer, director or producer category for its writer John Donnelly and director, Ben A Williams.
'Exciting year for film'
This year's nominations were announced by Dominic Cooper and Game of Thrones star Sophie Turner at Bafta's central London HQ.
Cooper said he could understand why people were "raving" about La La Land, praising its "gorgeous, skilful performances".
Amanda Berry, chief executive of the British Academy of Film and Television Arts, said it had been "a really exciting year for film".
"The range of films is quite extraordinary," she told BBC Breakfast. "That's what makes this year's nominations so intriguing and interesting."
Bookmaker Coral makes La La Land 1-5 favourite to be named best film and tips Chazelle to be crowned best director.
It also predicts Casey Affleck will win best actor for Manchester by the Sea and that Stone will beat Portman to the best actress prize.
The nominations follow last week's unveiling of the five actors in contention for this year's Rising Star prize.
A public vote will decide whether Laia Costa, Lucas Hedges, Tom Holland, Ruth Negga or Anya Taylor-Joy receive the award.
The 2017 Bafta Film Awards will be held at the Royal Albert Hall in London on 12 February.(BBC)