The stars, who are both outspoken activists on social issues, took to the stage in front of an estimated 60,000 protesters to campaign against welfare cuts and changes to the National Health Service (NHS).
Bragg performed a set of his hits before the march began, while Church gave a speech rallying against the country's political leaders.
"The government is firmly and unashamedly in the pocket of energy companies and big corporations and media moguls," she said.
"Our democracy is under threat from all sides. That's why it's so moving to see this many people standing up for what is right and just. Equality, egality, humanity and democracy. This is not a radical fringe but a growing social movement."
During the demonstration, organised by the People's Assembly Against Austerity, Church carried a hand-painted cardboard placard quoting physicist Albert Einstein. It read, "A foolish faith in authority is the worst enemy of truth."
Speaking of the reasons behind her activism, she told a press conference, "This Tory (Conservative) Government are (sic) using the idea of the debt to put forward these really hardcore ideological choices about shrinking the welfare state, cutting benefits for the most vulnerable and poorest in our society, and considering we are one of the richest nations in the world, I think it's absolutely obscene."
Church is set to perform a protest gig with Super Furry Animals on Monday night (05Oct15) in Manchester, England, where Britain's Conservative party is holding its annual conference.