Post Office campaigner Alan Bates was knighted in recognition of his campaigning work which highlighted the Post Office Horizon scandal.
Artist Tracey Emin, actress Imelda Staunton and fashion accessories designer Anya Hindmarch were all made dames in the list, while writer Armando Iannucci was made a CBE and cyclist Mark Cavendish was knighted.
Singer Rebecca Ferguson, Duran Duran frontman Simon Le Bon, Countdown's Susie Dent and Strictly Come Dancing's Amy Dowden were among the showbiz names to be made MBEs.
In the sporting world, former cyclist Chris Boardman and former Liverpool midfielder Graeme Souness were made CBEs, while former England footballer Karen Carney was made an OBE.
More than 1,000 people from across the UK received honours in Friday's list.
Sir Alan, the founder of Justice for Subpostmasters Alliance who was played by Toby Jones in an ITV drama about the scandal, said he was "honoured" by his knighthood.
The former subpostmaster, who previously rejected an OBE honour, told the PA news agency: "The time I was asked about the OBE... I felt it would have been quite offensive to many of the group if I'd accepted it.
"But I do know that I've had hundreds of emails and letters of support over the years and a lot of people do seem to think that I should receive some sort of recognition for the work that I've done for them or on their behalf.
"I know I'm the recipient of it and all the rest of it, but it's on behalf of the group as well - and recognition of the horrendous things that have happened to them and the story's not over yet."
Sir Alan said many people were "still suffering" and the campaigners would go back to the courts if necessary, adding "if we need to raise the funding for doing such a thing, I'm sure the nation will support us".
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Former Labour leader Mr Brown said he felt "slightly embarrassed" about being made a Companion of Honour, which is limited to just 65 people at any one time, adding that he preferred to recognise "unsung, local heroes".
Dame Tracey, who is known for her autobiographical and confessional artwork, said: "Dame Tracey has a good ring to it. I'm very, very happy. Another brilliant surprise in my life."
The Crown actress Dame Imelda said she was "thrilled" to be made a dame for her services to drama and charity.
She said: "I feel genuinely humbled to be recognised on the same level as the amazing actresses, all the great dames, who have led the way for so many of us."
Cycling sprint star Cavendish, 39, who is on the overseas list under his Isle of Man address, said he was "truly humbled" to be knighted.
He said: "It's always been the biggest privilege to represent my country, and seeing cycling as the sport, pastime and mode of transport I've given my life to, grow in Great Britain during the span of my career, has given me joy and pride beyond words."
The Thick Of It creator Iannucci said he was "proud" to work in the British television and film industry.
He added: "It's the best in the world, yet weirdly I've been spending more and more of my energy defending our public service television from attacks on its independence and funding.
"I'll take this award as a cue to keep going."
Professional dancer Dowden, who was diagnosed with Crohn's disease at the age of 19, said being made an MBE for raising awareness of inflammatory bowel disease was "beyond my wildest dreams".
Dowden, an ambassador for Crohn's and Colitis UK, said: "I accept it on behalf of all those who live with Crohn's disease, and will continue campaigning to raise awareness for and research into this terrible chronic illness."
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Lexicographer Dent, who appears in Countdown's Dictionary Corner, said she would celebrate her honour "on behalf of word lovers everywhere".
She added: "I'll do my very best to continue spreading the word, quite literally."
Duran Duran singer Le Bon said being made an MBE was "incredible" and "totally unexpected".
He added: "These last few years have been some of the most important in Duran Duran's career, and this is a bright but humbling highlight as our journey continues."
Choreographer Wayne McGregor, composer John Rutter and historian Niall Ferguson were all also knighted in the list.
Resident choreographer of the Royal Ballet Sir Wayne said it was an "incredible honour" and choral music composer Sir John said he "never dreamed" that music would "bring me the honour of a knighthood".
London Stock Exchange chief executive Julia Hoggett was made a dame and financier Bill Browder was given a knighthood for his human rights and anti-corruption work as head of the Global Magnitsky Justice Campaign.
Revenue and Customs chief executive Jim Harra was also made a Knight Commander of the Order of the Bath, which recognises the work of senior military officials and civil servants.
The youngest recipient in the list was 20-year-old Shamza Butt who received a British Empire Medal for her work at the voluntary development programme National Citizen Service on behalf of young people.
Harold Jones was the oldest recipient, who at 100 years old received a British Empire Medal for his fundraising for motor neurone disease charities in Sutton Coldfield in the West Midlands.
Award organisers said 64% of recipients were people who showed "outstanding work" in their communities either in a voluntary or paid capacity, adding that 66% of recipients lived outside London and the South East.
Of the 1,077 people honoured in the 2024 list, 509 were women - representing 48% of the total - and 10% of all successful candidates were from an ethnic minority background.
At CBE level and above, 40% of recipients were women.
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