The official publication of all 646 MPs' claims under their second homes, office costs and communications allowance were published on Thursday on the Parliament website.
But Freedom of Information campaigners criticised the vast amounts of information that were removed - including addresses, suppliers and some explanatory notes.
Among the more bizarre decisions was the removal of Environment Secretary Hilary Benn's first name, but leave the words "Mr" and "Benn" around the blacked out bit.
Asked why a reference to Sky TV - in a claim for a subscription - had been removed from his own claims, Mr Brown said he did not ask for it and he did not know why Commons staff had done so.
Labour MP Sir Stuart Bell, who sits on the Members Estimates Committee, initially said "private" information that had been removed was covered by the Data Protection Act.
However shown an almost entirely blacked out page by the BBC later, he said: "I think it's pathetic, I think it's unfortunate and I think it's officialdom and no MP would have authorised that. It simply adds to the discredit of the scandal of expenses."
Liberal Democrat leader Nick Clegg told the BBC the way receipts had been published "damages public faith in what MPs do even more".
The heavily censored publication yesterday of MPs expenses did nothing to improve the reputation of Parliament
"If only this information was available to them, then we wouldn't have found out about, for instance, the way MPs have been flipping from one property to the next ... in order to make personal gain.
"And that's why we now need complete change, not just in the expenses regime but in the culture of secrecy that still prevails at the heart of Whitehall and Westminster."
A spokeswoman for the Commons authorities confirmed that MPs' expenses for this year would be published in the same format, without addresses.
But Mr Cameron says he will press the Commons authorities to allow address details of MPs to be published, without the number of the house or flat.
He said only telephone numbers, bank details and "information with legitimate security concerns" should be routinely removed.
He said: "I have long argued that transparency is the key factor in restoring trust to our political system.
"The heavily censored publication yesterday (Thursday) of MPs expenses did nothing to improve the reputation of Parliament.
"After discussions with me, shadow leader of the House Alan Duncan will do all he can to push the House of Commons Commission to bring forward the publication of the 08/09 expenses in an uncensored form."
He said all Conservative shadow ministers had been asked to publish all "significant correspondence and receipts" alongside claims they are already publishing online.
He said he was determined that the Conservative frontbench be "as transparent as possible" to rebuild trust between the public and politicians.
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