David Blunkett has done the "honourable thing" in resigning as home secretary, his Tory shadow David Davis has said.
The Tories say Mr Blunkett had done the right thing
Mr Davis said he felt "very sorry" for Mr Blunkett adding that it was a "sad day" for a "remarkable man".
Lib Dem home affairs spokesman Mark Oaten said the resignation over the fast-tracking of a visa was a "personal tragedy" for Mr Blunkett.
Tony Blair said Mr Blunkett left the government with his "integrity intact" and "achievements acknowledged".
Mr Blunkett quit when it emerged in an e-mail that a visa for the nanny of his former lover, Kimberly Quinn, was fast-tracked.
Tory Mr Davis paid tribute to Mr Blunkett saying he was a "tough opponent".
But added that he had quit because the he realised the Budd inquiry into his involvement the visa application would "find against him".
"These have been a miserable few weeks and I suspect months for him, particularly after the allegations surfaced.
"He did the right thing. I feel very sorry for him. He is a tough opponent
and a remarkable man. It is a sad day for him."
Mr Oaten, for the Lib Dems, said the resignation had become "inevitable".
"A government which is seeking to highlight the home affairs agenda in the run up to a likely general election, was never going to be able to sit
comfortably with a home secretary so damaged in his office by a series of
personal misjudgements and who was so damaging in his assessments of his own colleagues."
He also urged whoever succeeded Mr Blunkett to build a "cross-party consensus"
Charles Clarke who takes over from Mr Blunkett said he had been an "an absolutely outstanding home secretary".
"His achievements have been tremendous and I will have a very hard act to follow in following David.
"I wish him the best in his own life. I am a close friend of his and I think
it is very, very important that everyone understands what a fantastic
achievement he has brought about."
Home affairs select committee chairman John Denham also paid tribute to Mr Blunkett saying his resignation was an "enormous loss" to the government.
"He set an agenda for Labour that I am sure we are going to follow in the years ahead."
But Scottish National Party leader Alex Salmond said the resignation "laid bare the deep divisions in government".
He said: "It is significant that David Blunkett has resigned, not because of
any wrong doing but because of the revelations in a book about the home
secretary, which demonstrated the deep divisions in the Cabinet."