The three were in a delegation of eight women - also including the editor of Marie Claire magazine, Marie O'Riordan and Vera Baird, the Labour MP for Redcar - that met the prime minister at Downing Street.
Ms Suu Kyi, the general secretary of the National League for Democracy in Burma, has been in and out of detention since 1989, and has become a global icon of democracy for her non-violent struggle against the country's military junta.
Her current period of house arrest began in May 2003 after the regime's militia attacked her convoy and killed up to 100 of her supporters.
Campaigners for her release say she leads an isolated existence with no visitors or phone line, that her post is always intercepted, and that armed guards keep watch on her.
The Burma Campaign UK organised today's Downing Street visit to urge Mr Blair to take more action to secure Ms Suu Kyi's release. It was part of international campaigning ahead of her 60th birthday on June 19.
According to the group, imports from Burma have more than tripled since Mr Blair came to power in 1997.
There have been calls for the UN security council to face up to Chinese pressure to hold a full debate about the situation in Burma and consider action including a ban on new investment and the exports that provide the regime with most of its income.
In December last year, the US called for Ms Suu Kyi to be released after it emerged that her period of house arrest was to be extended.
Mrs Kinnock - who led the group and delivered a letter to Mr Blair - said before the meeting: "Aung San Suu Kyi stands firm against one of the most brutal dictatorships in the world, and strikes fear into their hearts.
"On June 19, she will spend her 60th birthday in her home with no visitors, no telephone line and guarded by barbed wire and armed patrols.
"The world has stood idly by for too long - it is time for action. Unless there is concerted pressure on the regime, Aung San Suu Kyi could spend the rest of her life in detention. The prime minister will have to use his influence to secure the release of Aung San Suu Kyi and all political prisoners in Burma."
Brand said Ms Suu Kyi was a "brave and determined woman" who was "taking on one of the most brutal dictatorships in the world". "She has asked for our support, and she must get it," she said.
Ms Suu Kyi, the daughter of the late Burmese nationalist leader, General Aung San, was awarded the Nobel peace prize in 1991.
She lived abroad for much of her early life, studying at Oxford University, but returned to Burma to care for her ailing mother in 1988. She became involved with the campaign for democracy, and the military junta called general elections in 1990.
Ms Suu Kyi's National League for Democracy party won the election, and she should have become prime minister. However, the military refused to hand over power and nullified the result. Her earlier periods of house arrest were between 1989 and 1995 and 2000 and 2002.
Her late husband, the British lecturer Michael Aris, was diagnosed with prostate cancer in 1997. The Burmese government denied him an entry visa and Ms Suu Kyi remained in Burma, not meeting him again before he died in 1999. She continues to be separated from their children in the UK.
A report by Human Rights Watch, published yesterday, said Burma's military continued to kill, rape and conscript impoverished ethnic Karen villagers.
The New York-based organisation urged the junta to allow humanitarian agencies unfettered access to villagers who had been forced to flee by troops pursuing rebels through the jungles of eastern Karen State, which borders Thailand.
Karen guerrillas have been fighting for independence from Burma for more than five decades. Peace talks began in 2003 and later reached a provisional truce, but sporadic fighting has continued.
