Cameron had to admit his original plans to get the overseas territories and crown dependencies, including the British Virgin Islands, to have public registers have been shelved.
Cameron said that there needs to be consensus on the issue of tax, after Labour and Conservative governments both left crown dependencies and overseas territories to their business, but his government had changed this, pushing for registers of ownership.
But the Labour leader questioned whether the dependencies and crown dependencies were going to provide this information.
Cameron said: "I accept they are not going as far as us because we are publishing a register of beneficial ownership, we'll be one of the only countries in the world to do so. What the overseas territories and crown dependencies are doing is making sure we have full access to registers of beneficial ownership to make sure people aren't evading their taxes".
But Corbyn said that Cameron said that he would push for a public document.
Cameron said he had taken the unprecedented step, but overseas territories and crown dependencies were not forced to have a public register, as some of them may have walked away from the co-operation altogether.
On other issues of tax, Cameron failed to respond to the voting record of Conservative MEPs on multinational taxation in the EU, which planned for country-by-country tax reporting.
Meanwhile, Cameron confirmed that in the event of Brexit he would oversee the EU-UK negotiations, when probed by Ukip MP Douglas Carswell.
Carswell asked if the Prime Minister would stay in office to implement the decision the public comes to in the referendum. Cameron has a simple reply: "Yes."