Sir Paul said that he recognised the minister’s “frustration (and) irritation” that the claims had originally been approved by the now-discredited Commons fees office, but added: “I can not intervene”.
The former judge also rejected Mr Malik’s challenge to a demand to return overclaims for council tax, which he said he had “planned” with the consent of the fees office to offset a “shortfall” in mortgage interest claims.
John Lyons, former Labour MP for Strathkelvin and Bearsden, was ordered to repay £11,004.50 after Sir Paul said it appeared that he had claimed for his full mortgage costs, rather limiting his expanses to the interest only element to which he was entitled.
Labour's Derek Wyatt had his repayment demand reduced from £3,611 to £3,490 after Sir Paul rejected the bulk of his appeal.
In total, five MPs had their appeals rejected, while five more were upheld and four had their repayment requests reduced.
The Members Estimates Committee of senior MPs disclosed that 13 MPs with overclaims of £10,000 or more had entered into secret deals to delay their repayment requests until July.
Sheree Dodd, a spokesman for the House of Commons, refused to give their names or details of their overclaims.
Around half are expected to resign or lose their seats at the general election, which is widely expected in May – they will have any outstanding sums docked from the generous retirement grants given to MPs.
In addition, three former MPs are understood to be in the process of returning funds, while another two are said to be refusing to pay amounts running into tens of thousands of pounds.
A source said: “They haven’t quite said **** *** but they’re not far off.
“Some of the MPs wanted far longer than to repay their overclaims, but we had to have a cut off point, and July seems fair.”
Miss Dodd would not give the names of the former MPs who had failed to return overclaims.
Matthew Elliott, Chief Executive of the TaxPayers’ Alliance, said: “Taxpayers will be angry that the Commons authorities are still covering up information about the expenses scandal.
“Any delay will mean that MPs’ continue to benefit from their dodgy claims for months to come and might allow them to avoid paying at all, or to pay out of the resettlement grant they shouldn’t be getting in the first place.
“They need to name the MPs who are delaying paying back taxpayers’ money that should never have been paid out and outline why they have been allowed a delay, or make it very clear how they will ensure that the money is definitely repaid.”