"I would hope that Jacqui Smith would tell the truth, which presumably can be backed up with police logs and she can say how many nights she spends in the house in London."
The couple initially contacted Conservative leader David Cameron by e-mail about their concerns, Tory sources have confirmed - prompting Labour claims their complaint is politically motivated.
Mr Cameron's office told the Taplins it was not a matter for them but suggested they might wish to contact a newspaper as this would be "in the public interest".
The couple then spoke to the Mail on Sunday, which ran a story on their allegations at the weekend, before making a complaint to the Standards Commissioner.
Mr Lyon has previously turned down two requests to investigate Ms Smith over her decision to designate her sister's house - where she stays when she is in London - as her main home, but his decision to formally accept this latest complaint could lead to a full investigation.
Jacqui Smith's decision to call her sister's home her main residence has enabled her to claim at least £116,000 in second home allowances on her constituency home in Redditch, Worcestershire, since becoming an MP.
Ms Smith has consistently denied any wrongdoing, insisting that she has written approval from the Commons fees office for her arrangements.
Jacqui Smith says she's 'done nothing wrong' but that's not how the public see it
Norman Baker, Lib Dem MP
She told BBC News: "I followed the advice I was given and I have followed the rules," adding that she would "respond to any questions the independent commissioner asks me".
Sources close to the home secretary have told BBC News that she paid rent to her sister at a market rate and that her sister paid full tax on the income.
They add that Ms Smith does not simply rent one room and that her children come to stay at the London address, including over Christmas and the New Year.
Sources claim she spends the bulk of her time in London but had asked the police to maintain a "low profile" so the neighbours may not have realised she was in residence.
The fees office had told her it was "irrelevant" to an allowance claim where her family lived - it was all about where she spent most of her time, they say.
Mr Lyon has asked Ms Smith to set out exactly how much time she spends at the address in south-east London.
Commenting on the affair on BBC Radio 5 Live, David Cameron said: "I think that what we need to know is what is her main home."
He added that it was necessary to establish whether Ms Smith's arrangement was "reasonable", saying: "I think the home secretary has some questions to be asked on that front."
Lib Dem MP Norman Baker, who campaigns for greater parliamentary accountability, welcomed Mr Lyon's decision to look into Ms Smith's allowances - and called for a tightening of the rules surrounding second home allowances.
"There is clearly an opportunity for MPs to designate their first and second homes in order to maximise financial advantage, which cannot be right."
He added: "Jacqui Smith says she's 'done nothing wrong', but that's not how the public see it."
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