Mr Hogg was one of several Tories whose claims were questioned
Conservative MP Douglas Hogg has agreed to repay £2,200 - the cost of clearing his moat at his country estate - amid the continuing row over MPs' expenses.
Mr Hogg maintained he had not claimed the money but agreed it had not been "positively excluded" from paperwork submitted to the Commons fees office.
"I believe that my claims fell clearly within the scope of the rules."
He is the latest in a string of Labour, Tory and Lib Dem MPs to pay back money after claims came to light.
Mr Hogg was irritated by the Telegraph's coverage of his own claims - which was included in a series of articles about how wealthy Conservatives had claimed towards the cost of maintaining large constituency homes.
He said 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.
Several Tory frontbenchers have agreed to repay claims - including a £2,000 bill to repair a pipe under a tennis court claimed by Oliver Letwin and £5,000 claimed for gardening costs by Alan Duncan.
In a statement, Mr Hogg said he supported party leader David Cameron's efforts in addressing the issue.
"I believe that my claims fell clearly within the scope of the rules," he said.
"However, we politicians have got this wrong and I apologise for that fact. The public have lost confidence in the system and we must put that right."
He added: "I recognise that the clearing of the moat was not positively excluded from the claim, and in recognition of the public concern over this issue I will repay £2,200 to the Fees Office."
He also said he would make no further second homes allowance claims during this Parliament, "by which time I hope that new and more acceptable rules will be in place".
Mr Hogg's local Conservative constituency association in Lincolnshire issued a statement of support for the MP saying it believed he had "addressed the concerns of his constituents and public opinion" and "continues to enjoy the association's complete confidence".
Greg Barker, the shadow climate change minister, was reported to have bought a flat with the help of taxpayers' money and sold it after just 27 months at a £320,000 profit.
He said that profit had been "greatly exaggerated" and did not take account of the fact he had paid "a substantial six figure sum" to carry out "major works".
But he said he was "mindful of the example set by David Cameron and the shadow cabinet" and would pay capital gains tax on the properties.
Meanwhile Michael Ancram, another Tory grandee and the marquess of Lothian who had already agreed to refund a £100 claim for repairing a swimming pool boiler, said he would make no further claims under the second homes allowance.
He said: "I completely support and endorse David Cameron's response to the unacceptable situation surrounding MPs' claims."
Earlier Mr Cameron's aide Andrew MacKay quit over what the party called an "unacceptable" claim - he is married to a Tory MP and both claimed almost the full amount for two addresses.
Among Labour MPs who have agreed to pay back money are Communities Secretary Hazel Blears, who has paid £13,332 in respect of capital gains tax on the sale of her second home.