Mr Hoon apologised for the bills and has repaid £384
Transport Secretary Geoff Hoon has become the second cabinet minister in 24 hours to repay money he claimed on his designated second home.
Mr Hoon claimed bills in advance for a full year on his Derbyshire property - but in the same year he claimed a different house was his second home.
It was an "inadvertent administrative error", he said, and apologised.
Alistair Darling repaid £668 of his own advance payment but the Lib Dems say the chancellor should be dismissed.
In a series of interviews on Monday, Gordon Brown said Mr Darling had made an "inadvertent" mistake and did a "great job" as chancellor.
Mr Darling told the BBC he had always tried to do the "right thing" and it was upsetting when his integrity was being "impugned".
But he said he accepted that he should pay back some of a £1,000 service charge - an advance payment for six months on a flat he moved out of shortly afterwards.
BBC political editor Nick Robinson said words used by both Mr Brown and Mr Darling seemed to indicate their long partnership was preparing to end - Mr Brown is expected to reshuffle his cabinet next week.
Conservative leader David Cameron told the BBC the chancellor was "clearly in serious difficulties".
Lib Dem Treasury spokesman Vince Cable went a step further by saying the guardian of the nation's finances had to be "regarded with moral authority, not just operating within technical rules, by the financial community and the country at large. I don't think the chancellor is in that position".
Both Mr Darling and Mr Hoon are among ministers accused of "flipping" their second homes - repeatedly changing the designated second home on which they could claim expenses.
Mr Darling, who switched the designation to four properties in four years, told the BBC on Monday he had only changed his second home to accurately reflect where he was spending the most time.
The Daily Telegraph accused both Mr Darling and Mr Hoon of claiming on two homes at the same time - they dispute this.
In its report on Tuesday, the newspaper says Mr Hoon changed his second home from Derbyshire to a London property during the course of 2006.
But he had claimed back bills for a full year's insurance, a gas service contract and a TV licence on the Derbyshire property - it reports he claimed for three TV licences in one year on expenses.
MP referred to panel
Mr Hoon said the three bills had been settled before he knew he would be moving and were usually paid annually. He has paid back £384.
He said there had been "an entirely inadvertent overlap in bill payments. This was entirely accidental".
He added he had repaid the money which covered the months he no longer claimed the Derbyshire property as his second home as soon as it was drawn to his attention.
"Although this was an inadvertent administrative error, I unreservedly apologise for the mistake," he said.
MPS LEAVING PARLIAMENT
The following MPs have said in the past three weeks that they will not contest the next election
Conservative: Andrew MacKay, Julie Kirkbride, Douglas Hogg, Sir Peter Viggers, Anthony Steen, Sir Nicholas and Ann Winterton, Christopher Fraser
Labour: Margaret Moran, Ben Chapman, David Chaytor, Ian McCartney, John Smith, Patricia Hewitt, Beverley Hughes, Michael Martin (Speaker)
Mr Cameron said the scandal was "getting worse", and the public felt "locked out" of the system.
He added: "They want their say, and that's why I think that the cleansing process of British politics does require a general election to take place in fairly short order."
Meanwhile Labour backbencher Jim Devine has become the latest MP to be referred to the party's special endorsement panel, which will look into his expenses claims and consider whether he should stand as an MP again.
He was accused of buying fellow MP Michael Connarty's furniture from him - and claiming it back on expenses.
And Bury North Labour MP David Chaytor, accused of claiming for a mortgage that was already paid off, has announced that he will not stand at the next election.
Former Health Secretary Patricia Hewitt has also said she will stand down as an MP at the next election but has said the move has nothing to do with the expenses furore.
Shortly afterwards children's minister Beverley Hughes became the latest to announce she would stand down, in her case due to "family circumstances".