During 2004 and 2005 he was living in the Notting Hill property, he owned a flat in Pimlico - which is closer to Parliament - the newspaper reported.
At the time, it was within the rules - but the rules changed in July 2006 to stop MPs renting properties from close relatives.
He designated Mr Cash designated the flat as his second home with the Commons fees office and claimed more than £15,000 for rent - equivalent to about £1,200 a month.
Ms Cash - who stood as a Conservative candidate at the last general election - later sold the property for a £48,000 profit, the newspaper added.
It also reported that, after moving out, Mr Cash had nominated two private members' clubs as his "second home" for allowances purposes over three months.
'Pay the price'
Mr Cash, an MP for 25 years, who is best known for his Eurosceptic views, told the BBC that he had shown the tenancy agreement to the Commons authorities and it had been approved.
He told the BBC: "I was within the rules under a tenancy agreement that was agreed in advance with the Fees Office."
He also said that he had never claimed any allowances for his much larger main house in Shropshire, which would have cost the taxpayer much more.
He told the BBC he had not rented out his own London property while living at his daughter's flat.
"The taxpayer was no worse off than they would have been if I had been renting it from anyone else."
The Telegraph reported that Mr Cash indicated he would repay any money if asked to do so by the Conservative Party.
Since the Telegraph began its series of stories about what MPs have claimed, based on leaked receipts, 11 MPs have said they will stand down at the next election - some have said they are standing down for other reasons.
Conservative MPs Julie Kirkbride and Christopher Fraser and Labour's Margaret Moran said on Thursday they would not defend their seats at the next election although all say they have done nothing wrong.
Mr Fraser said he was standing down for personal reasons to care for his ill wife.
Tory leader David Cameron has said all his MPs must justify their expenses claims to their constituents.
The idea that we're turning a blind eye to it, we don't think it's serious, we hope it'll all be swept under the carpet, that is not our approach at all
Harriet Harman Labour deputy leader
Eight Conservative MPs have already announced they will be standing down and some have repaid money claimed.
Two Labour MPs have been suspended from the Parliamentary Labour Party and four others have announced their intention to stand down. Speaker Michael Martin is also standing down.
Labour's deputy leader Harriet Harman told the BBC on Friday that Labour MPs had to answer to their constituents.
She said: "The idea that we're turning a blind eye to it, we don't think it's serious, we hope it'll all be swept under the carpet, that is not our approach at all."
"If people have done wrong they have got to pay the price for that. We're saying it's not just that people have got to have made their claims in good faith, but they've got to have exercised good judgement because that's how their constituents will judge them."
Several MPs have been accused of avoiding paying capital gains tax on properties they had designated as their second homes for expenses purposes. There have also been questions over MPs who have claimed for tax advice on expenses.
Ms Harman said: "If there's tax to be paid, it's got to be paid. We actually set the taxes so we're the first people who should be paying them."
On Friday the Telegraph reported that Labour MP Nigel Griffiths claimed £3,600 for a digital TV and radio set which was rejected.
Mr Griffiths said the Commons authorities had turned down the claim for a TV and radio and he had bought the items without spending any public money.
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