Waller-Bridge is up for a lead actress prize for Fleabag, while her Irish co-star Andrew Scott is also nominated.
Marriage Story, a Netflix production, is the most nominated film, having received six citations in all.
The Irishman, another Netflix film, and Quentin Tarantino's Once Upon a Time in Hollywood, have five nominations each.
The Crown, Chernobyl and US crime thriller Unbelievable lead the way on the TV side of things, having received four nominations apiece.
Marriage Story and Martin Scorsese's The Irishman are both up for best film drama, as are Joker, The Two Popes and Sam Mendes' World War I epic 1917.
Tarantino's film is up for best musical or comedy, alongside Nazi satire Jojo Rabbit, murder mystery Knives Out, Elton John biopic Rocketman and comic biopic Dolemite Is My Name.
Golden Globes: 2020 nominees in full
Scorsese, Mendes and Tarantino are up for the best film director award, with Joker's Todd Phillips and Parasite's Bong Jong Ho completing the all-male line-up.
The South Korean film-maker is also up for best screenplay for Parasite - a dark comedy about his homeland's social divides that is also up for best foreign language film.
Analysis by Lizo Mzimba, BBC entertainment correspondent
Netflix has been throwing huge amounts of cash at both making and marketing its awards hopefuls this year. With that kind of spending, the streamer will be hoping for not just a good, but a great return on its investment. At this stage of awards season, it potentially looks like it might pay off.
The film with the most nominations is Netflix's Marriage Story, starring Adam Driver and Scarlett Johansson, which has six. Just behind with five, another Netflix production - Martin Scorsese's epic The Irishman starring Oscar winners Robert de Niro, Joe Pesci and Al Pacino.
It's still early days though. Last year, the Dick Cheney biopic Vice led the way with six Globe nominations and went on to win a grand total of one Academy Award (for make-up and hairstyling). Still, for the last few years, the eventual best picture winner at the Oscars has come from one of the films with either the most or almost the most nominations at the Globes.
The Globes' real power comes less from those who decides on the winners but rather from its position in awards season. While it may from time to time make some unusual choices, it gives some films the chance to build momentum at the crucial time when Oscar voters are deciding not only which films to vote for, but just as importantly, which films they'll actually make time to see.
And in what can be a tight race, just having a film labelled as a Golden Globe nominee or winner can make a difference.
Christian Bale is in the running for the best actor in a film drama award for Ford v Ferrari - released as Le Mans '66 in the UK.
Bale's competition includes fellow Brit Jonathan Pryce for The Two Popes, as well as Antonio Banderas, Adam Driver and Joaquin Phoenix for Pain and Glory, Marriage Story and Joker respectively.
Daniel Craig is up for best actor in a film comedy or musical for Knives Out, as is Egerton for Rocketman and Jojo Rabbit's young British lead Roman Griffin Davis.
Leonardo DiCaprio and Eddie Murphy are also nominated in this category, for Once Upon a Time in Hollywood and Dolemite Is My Name respectively.
The best actress in a film drama shortlist includes Britain's Cynthia Erivo for Harriet, a biopic of anti-slavery activist Harriet Tubman.
Erivo's competition includes Scarlett Johansson for Marriage Story, Saoirse Ronan for Little Women and Judy's Renee Zellweger - widely considered to be the favourite for both this award and 2020's best actress Oscar.
The best actress in a film comedy or musical shortlist includes Dame Emma Thompson for Late Night and The Farewell's Awkwafina.
I'm Gonna Love Me Again, a new track written for Rocketman by Sir Elton John and Bernie Taupin, is up for the best original film song award.
So is Beautiful Ghosts, written by Taylor Swift and Andrew Lloyd Webber for the upcoming film version of Cats.
It is the only nomination for Cats, which has been left out of the major categories despite reports it was screened for voters at the last minute.
Swift expressed delight on Twitter that "one of the most fun, fulfilling creative experiences" in her life had been recognised by the Hollywood Foreign Press Association (HFPA).
Into the Unknown from Frozen 2 and Beyonce's song Spirit from Disney's The Lion King also make the cut.
Both films are up for best animated film - an award The Lion King will not be eligible for at the Oscars or Baftas, as it was not submitted for consideration.
The remake of Disney's 1994 animation uses computer animation to create photorealistic facsimiles of real-life animals.
Olivia Colman, Helena Bonham Carter and Tobias Menzies are all up for awards for their royal roles in the latest series of The Crown.
Colman is up for best actress in a TV drama, where her competition includes Killing Eve's Jodie Comer and the stars of Apple TV series The Morning Show - Jennifer Aniston and Reese Witherspoon.
Dame Helen Mirren, Kit Harington, Emily Watson and Sacha Baron Cohen are among other British actors who are up for TV prizes.
Harington's consideration for best actor in a TV drama is the only nomination for the final series of fantasy saga Game of Thrones.
Overall there are 27 Britons in contention for the awards, which recognise both film and television.
Netflix - the streaming giant behind Marriage Story, The Irishman, The Two Popes and The Crown - has 34 nominations in all - 17 each for film and TV.
HBO have 15 TV nominations, four of them coming for their mini-series about the Chernobyl nuclear disaster.
Ricky Gervais will return to host the awards on 5 January, having previously hosted them in 2010, 2011, 2012 and 2016.
Tom Hanks will receive a lifetime achievement award at the event, following in the footsteps of such recent honourees as Meryl Streep and Oprah Winfrey.
Hanks is also nominated for a best supporting actor prize for his role as children's TV star Mr Rogers in A Beautiful Day in the Neighbourhood.