Former prime ministers Tony Blair, Gordon Brown and David Cameron have joined hundreds of people to celebrate the life of Dame Tessa Jowell at a memorial service in London.

Leaders from across the political spectrum united to remember the former culture secretary at Southwark Cathedral, where more than 1,000 people came together on Thursday to pay their respects to Jowell, who was a driving force behind the 2012 London Olympics.

Her daughter, Jessie Mills, recalled her mother’s “endless, heart-bursting, infinite love”. She told the service: “To be loved like this since the moment we were born and to be her children is the single greatest privilege of our lives.”

Jowell’s husband, David Mills, said his wife’s last words were “love forever”. “To know that she was held in such high esteem, was loved by so many ... all that is a consolation which will in some measure always beguile our grief,” he said.

Blair paid tribute to his friend and former colleague. Not a day went by when he did not think about her, he said. She was “unafraid to stand up for her friends, unafraid to stand up to them, but always standing by them”.

‘I resisted, she persisted, I desisted’: Tony Blair on being persuaded London 2012 was a good idea. Photograph: Stefan Rousseau/PA

Blair drew laughter as he recalled how she had persuaded him of the merits of hosting the 2012 Olympics, her “brainchild”. “I resisted, she persisted, I desisted,” he said.

“Tessa died with so much still to give, but if life is measured not in how long you live but by how much you give, she lived a length of biblical proportions.

“Tessa, we love you, we thank you and we will never, ever forget you.”

The former Labour leader Ed Miliband, the former home secretary Lord Blunkett, the mayor of London, Sadiq Khan, the Commons Speaker, John Bercow, and the London 2012 chairman, Lord Coe, also attended the service.

The memorial came as Khan announced that a walkway at the Olympic Park would be named in her honour.

Tessa Jowell holds up her Dame Commander insignia at Buckingham Palace in 2013. Photograph: WPA Pool/Getty Images

Laughter rang out several times during the 90-minute service as colleagues remembered her insistence on holding multiple meetings and always being on a diet. The long queue around the cathedral’s perimeter an hour before the service started was testament to her enduring popularity.

Jowell died in May of a brain tumour that had been diagnosed the previous year.

A well-liked figure in parliament, she also championed the Sure Start initiative, which aimed to give children the best possible start in life through improvements and better access to childcare, early education, health and family support.

In the months before her death, she moved fellow peers to tears as she used the House of Lords as a platform to discuss her condition and call for patients to have better access to experimental treatment.