A former Labour MP faces several years in jail after becoming the first politician to be convicted of fiddling his parliamentary expenses.

David Chaytor, who had been due to stand trial on Monday, changed a previous plea as he admitted three charges of false accounting involving a total of £18,350 of expenses claims.

He claimed £12,925 in rent on a flat he owned and £5,425 for rent on his mother's house, and falsely charged £1,950 for computer support services.

The maximum sentence for the offences is seven years, but his guilty pleas could mean any term is reduced by one-third. Chaytor, who stood down as the MP for Bury North in May's general election, could be the first ex-MP to be jailed since Jonathan Aitken, the former Tory cabinet minister, was convicted of perjury 11 years ago.

Chaytor, 61, is among six former or serving politicians to face criminal charges arising from the expenses scandal of 18 months ago. He was remanded on bail to be sentenced at Southwark Crown Court on 7 January.

He claimed £12,925 between November 2005 and September 2006 for renting a flat in Westminster, which it turned out he owned. A fake tenancy agreement said he was paying £1,175 a month.

He also falsely claimed, between September 2007 and January 2008, some £5,425 for renting a house in Bury at £775 a month.

It emerged that the house was owned by his mother, who was in a residential home and suffering from Alzheimer's disease. She was never paid the money; moreover, he would not have been allowed to claim for leasing a property from a relative.

The charge relating to IT support services said he supplied two invoices from a man named Paul France, when "the services had not been provided or charged for".

Chaytor had pleaded not guilty to the charges in May, but changed his pleas yesterday at the Old Bailey. His change of heart came after a legal attempt to have the case dismissed – on the grounds that he should not be prosecuted because of Parliamentary privilege – failed.

His QC, James Sturman, told the judge, Mr Justice Saunders: "There are many misconceptions about the case which we will wish to put right on 7 January.

"Obviously he accepts this is a serious matter. There is no loss to the public purse. Any sums claimed have been, or will be, repaid."

Mr Sturman said £13,000 had already been paid.

He asked for a pre-sentence report and said he expected to call character witnesses during the sentencing hearing. He said there had so far been "a total failure to reflect that his case reflects appropriate claims gone about in the wrong way." Simon Clements, of the Crown Prosecution Service, said: "David Chaytor has admitted his dishonesty and will now face the consequences of his actions.

"No one, no matter what their position, should be allowed to take money they are not entitled to. By his actions David Chaytor has abused the trust placed in him by the public."

Hundreds of MPs were ordered to repay a total of £1.12m in the wake of the expenses scandal, which triggered a public outcry.

Others due to face separate trials involving their expenses are the former Scunthorpe Labour MP Elliot Morley, the ex-Labour MP for Livingston Jim Devine, the Barnsley Central Labour MP Eric Illsley, the Tory peer Lord Hanningfield and Lord Taylor of Warwick, a former Tory peer.

Chaytor, a one-time lecturer, was elected during Tony Blair's 1997 election landslide and spent 13 years on the back benches.

He was suspended by Labour and barred from representing the party again after details of his expenses claims emerged in May 2009.

He blamed the claims on "accounting errors", apologised and referred himself to the Parliamentary Standards Commissioner to be investigated over the affair.