Demonstrators converged on Trafalgar Square calling for increased investment in the health service, housing, education and public sector pay, as well as action to stop the loss of thousands of steel workers' jobs in Wales.
"No ifs, no buts, no public sector cuts," they chanted.
Some protesters also demanded Cameron quit following revelations that he had shares in an offshore fund set up by his late father, holding up banners saying "Ditch Dodgy Dave" and "Cameron Must Go -- Tories Out!".
The march was planned before Cameron's family finances were revealed in the so-called Panama Papers, but organising group The People's Assembly said it "proves that this is a government for the privileged few".
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Trade union leaders and politicians addressed the crowd gathered in a rainy Trafalgar Square, with the opposition Labour party promising to end years of austerity imposed following the global financial crisis.
Cameron said he sold his offshore holdings before taking office in 2010 and denied allegations that his father had set up his fund to avoid paying tax.
But the row has put the premier under pressure at a difficult time, as he seeks to manage an increasingly bitter fight within his Conservative party over the upcoming referendum on EU membership.
Some 128 of the 330 Conservative lawmakers in parliament and several of Cameron's own ministers are campaigning against him in favour of leaving the EU ahead of the June 23 vote.