The home secretary has denied helping to fast-track a visa application for his ex-lover's former nanny.
Mr Blunkett denies helping speed the visa application through
The allegation is one of several made in the Sunday Telegraph and, although any impropriety has been denied, Tory leaders want an independent inquiry.
David Blunkett is alleged to have used his position to help Filipina Leoncia Casalme, who worked for Kimberly Quinn, get permanent residency.
Prime Minister Tony Blair says he has "full confidence" in Mr Blunkett.
As well as the visa claims, reportedly made by Mrs Quinn in an e-mail, the Sunday Telegraph says Mr Blunkett, 57, shared confidential security information with her.
This included telling her parents to avoid Newark Airport near New York hours before a security scare.
Other claims include giving Mrs Quinn, 43, a first-class train ticket which had been assigned to him.
Kimberly Quinn reportedly made the claims in an e-mail
Mrs Quinn is publisher of The Spectator magazine, which is owned by the Barclay Brothers, who also own the Sunday Telegraph.
Ms Casalme left her employment two months ago and now lives in Dagenham, Essex.
Mr Blunkett's spokesman, addressing the visa application allegation, said the home secretary had checked the application form.
But he denied that it was processed through Mr Blunkett's office.
The spokesman said that information about the New York security scare was already in the public domain.
And he said that the train ticket was for MPs' spouses and Mr Blunkett and Mrs Quinn were in a "close relationship" at the time.
Mr Blunkett is quoted as saying that he was "very saddened that someone I cared so deeply for should seek quite erroneously, to damage my public position".
"This cannot be in the interests of any of us. I shall continue to keep my private life private and separate from my public duties," he added.
Shadow home secretary David Davis has called for a judge to carry out an independent inquiry into the newspaper allegations surrounding his relationship with Mrs Quinn.
He made clear he thought Mr Blunkett should consider resigning if the visa allegations were found to be true.
He told Sky News: "It is a very serious allegation. No home secretary could survive that."
Mr Blunkett's case was "similar" to that of former Northern Ireland Secretary Peter Mandelson, who resigned from the Cabinet after allegations that he tried to influence a passport application, Mr Davis said.
Liberal Democrat home affairs spokesman Mark Oaten said: "It is always sad when people's private lives encroach into the political world.
"On the particular allegations over granting a visa, the home secretary has denied any wrong doing and we accept that.
"But if further evidence emerges he will clearly need to make a fuller statement."
Immigration minister Des Browne, who works with Mr Blunkett, insisted there was "no impropriety" in his actions.
He confirmed it would be wrong for ministers to intervene in visa applications but said he did not believe this had happened.
He told Sky News: "I know David Blunkett very well. He is an honest, straightforward man. Whatever inquiries or investigations there need to be in relation to this, he will co-operate fully with.
"He has nothing to fear. There has been no impropriety."