The Telegraph has already published expenses claims made by Labour and Tory frontbenchers, including those for a lawnmower, dog food and changing light bulbs.
Among shadow ministers who have agreed to pay back some of the expenses claims they made are Michael Gove, Alan Duncan, Oliver Letwin and Andrew Lansley. Others have agreed to stop claiming allowances for second homes.
"We need money paid back now," Mr Cameron said as he outlined an overhaul of the rules his MPs would abide by in claiming expenses.
In future, Tory MPs will only be allowed to claim for basic costs on second homes such as rent and utility bills and not, as at the moment, for furniture or food.
In addition, he will bring in regulations on the designation of second homes, to prevent the practice known as "flipping" -which has allowed some MPs to maximise allowance claims, subsidise home improvements or avoid tax on home sales.
A new panel will also be created to scrutinise MPs' claims and to ensure they comply with the new standards, while all Tory MPs will be required to publish details of all future claims online.
If MPs who have made excessive claims refuse to pay back the money, Mr Cameron said they would lose the party whip.
"I don't care if they were within the rules," he said of claims made in the past. "They were wrong."
I want to say sorry it has come to this and sorry for the actions of some Tory MPs
"I want to say sorry that it has come to this and sorry for the actions of some Tory MPs," he added.
Mr Cameron defended his "robust" reaction to the expenses scandal, saying his reforms would ensure there would be no more "unreasonable" claims in the future and were designed to show his party "understood the public anger" about the issue.
But he said the Commons was "deeply mired" in scandal and that its reputation would have to be rebuilt "brick by brick".
Shadow chancellor George Osborne has agreed to pay back the £440.62 cost of a taxi journey between London and his Cheshire constituency after he missed the last train.
Mr Osborne said he wanted to make sure there were no "question marks" about his expenses but acknowledged the Conservatives were not "whiter than white".
Later Gordon Brown told the BBC's political editor Nick Robinson an independent group would scrutinise all MPs' claims over the past four years to see if they were made within the rules and could result in MPs having to pay money back, or facing disciplinary action.
He also said there would be restrictions on allowances on furniture and fittings and a clampdown on capital gains tax rules and he called for a cap on mortgage interest payments.
And Communities Secretary Ms Blears said she would pay £13,332 in capital gains tax. She came under fire after it emerged she had sold a flat she designated as her "second home" with the Commons, but did not pay capital gains tax on it.
She told Sky News it was her decision and said while she had "complied with the rules" she recognised the public were "really really angry" and therefore it was the "right thing to do" to pay the money.
The latest batch of expenses details revealed by the Telegraph included the fact that Peterborough MP Stewart Jackson had made a claim of £304.10 for the upkeep of a swimming pool.
He said "the pool came with the house and I needed to know how to run it" and he had agreed to pay back the money.
The pool came with the house and I needed to know how to run it.
Former shadow defence secretary Michael Ancram claimed almost £100 for the repair of a swimming pool boiler but said he had made a "genuine mistake" and would repay the money.
The newspaper also said North East Hampshire MP James Arbuthnot, chairman of the Commons defence select committee, had claimed £1,471 for garden and swimming pool costs. He has agreed to repay the swimming pool expenses.
Meanwhile, the Telegraph says former cabinet minister Douglas Hogg, MP for Sleaford and North Hykeham, submitted claims for more than £2,000 to clear a moat around his estate and £14,500 for a housekeeper.
But he told the BBC that, while he had claimed for a housekeeper, he had never asked to be reimbursed for the cost of cleaning the moat - it had simply been mentioned in details of expenditure on his house.
What was unthinkable just a few weeks ago has suddenly becomes unavoidable
Mr Hogg said all of his claims had been made with the prior agreement of the Commons fees office.
Deputy Commons Speaker Sir Alan Haselhurst, Tory MP for Saffron Walden, is reported to have claimed £142,000 on his country house, and £12,000 for gardening bills over five years.
He told the BBC he had claimed for £142,000 and had moved his second home allowance from London to his constituency when he became deputy speaker and believed the claim was within the rules.
The Telegraph says senior backbencher Sir Michael Spicer claimed more than £7,000 for his garden, including hedge-cutting for a "helipad" and £620 for rewiring and fitting a chandelier. He said he had no "helipad" and said the chandelier was a "modest" light fitting installed as part of an electrical safety refit.
The Telegraph reports that David Heathcoat-Amory, Tory MP for Wells, claimed more than £380 for horse manure for his garden.
It adds that former shadow home secretary David Davis claimed more than £2,000 on mowing and rolling his paddocks and £5,700 for a portico for his house in Yorkshire.
Mr Davis said he had not done anything wrong, but agreed the rules needed to be changed.
Meanwhile, Labour MP for Luton South Margaret Moran has issued a statement saying she will repay £22,500 used to treat dry rot at a property 100 miles from her constituency.
She previously said the Southampton house was necessary for a "proper family life" because her partner had worked there for 20 years.
On Monday Prime Minister Gordon Brown apologised on behalf of all political parties for MPs' expenses revelations over recent days, while Mr Cameron urged MPs to say "sorry" for the expenses system.
Liberal Democrat leader Nick Clegg said it must not be a "hollow apology" and must be followed by real change.
In other developments at Westminster the Tory MP Douglas Carswell is seeking support for a motion of no confidence in the Speaker of the House of Commons, Michael Martin, over the way he has handled the expenses furore.
And former Tory chairman Lord Tebbit urged voters to show their anger about the expenses scandal by not backing any of the major political parties in next month's European elections, a move which resulted in a public reprimand from Mr Cameron.
A ROUND-UP OF OPINION ON THE EXPENSES ROW
Columnists, commentators and bloggers express their opinions on the MPs' expenses row and speculate on what is in store for the Speaker Michael Martin.
Maybe he's most angry with himself. No, stupid idea. But he is the very man responsible. It's him. No other individual could have stopped the abuses, ordered the Fees Office to enforce the rules. He could have. He alone could have ordered the laundry washed in private and left office with a reformed expenses culture behind him.
At the heart of all this lies decades of political cowardice, where governments and MPs have conspired to repress MPs' basic pay, the visible part of their remuneration, in the belief that voters will never understand large pay increases for MPs and to give nods and winks to making good the pay deficit by a soft and exploitable - and until now - largely invisible expenses regime.
MPs are doing an important job and should be paid enough that high-quality people without independent means are financially able to do it. Being an MP is a public service and should not be a way to become rich. But nor should MPs earn only an average wage. Being an MP ought surely to pay as much as a GP or a secondary school head teacher.
Someone in his fifties who's raised a family, who's been a shop steward, or run his own engineering factory, or fought in a tank battle, or prosecuted murderers in front of a jury is not going to be terribly impressed or scared by the whips. But someone barely out of his or her teens who's been nothing more than another MP's dogsbody, or a 'special adviser,' or a local government official, is likely to be a pushover. He's an employee of the executive, anxious to please. And, like all employees who have sold a large chunk of his integrity in return for a quiet life, he'll expect something back for it.
New Labour MPs, with their home improvements and their little property empires use the expenses system to get away from the working classes as fast as they possibly can. Tory MPs with their moats and country homes and porticoes (whatever the hell they are) have already got away from the working classes as fast as they possibly could and now use their expenses to shore up the defences.
The key here is going to be how ruthless Cameron is with those on his Front bench team .This does of course assume that Cameron knows there are no elephant traps about the order of his own house waiting to surface.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.