Bernie Grant, Labour MP for Tottenham, said that British society was being given "a last chance" to improve race relations in light of the damning report of the inquiry into the death of Stephen Lawrence.
Speaking after the statement by the Home Secretary, Jack Straw, Mr Grant warned: "I'm not saying he should be sacked, I'm not saying that he should be resigning.
"I think early retirement is what should happen to Mr Condon [sic] because if we are to move into a new phase, we can't move into the new phase with the same old faces."
The "feedback from the street" was that while attitudes among officers on the beat had improved, the same could not be said of their supervisors, the desk sergeants and superintendents.
"That is the attitude that permeates institutionalised racism so we have to begin to call to account the actions of some of these detectives. The black community is looking very closely at that issue," Mr Grant said.
But Mr Straw insisted that Sir Paul had accepted the charge of institutional racism as defined in the report, and was "the man to take this forward". He reminded Mr Grant that Sir Paul was due to retire in 10 months' time.
Earlier, Sir Norman Fowler, the shadow Home Secretary, said it was society's aim to ensure that such an "appalling tragedy" never occurred again.
"I reassert our total opposition to racially prejudiced behaviour. It must have no place in the police. It must have no place in any other organisation public or private. It has no place in this country," he said.
As far as the police were concerned, there was an "urgent need to build trust where it does not exist and to rebuild trust where it has been destroyed". Sir Norman added: "There is a massive task and no one should underestimate what is needed."
But he expressed concern about the use of the phrase "institutional racism", which should not be used as a generalised condemnation of the whole of the service. "We will do everything to help in the reform process. What we will not do is to support any generalised attack on the police, who remain one of the best services we have in this country."
The Tory and Liberal benches were barely half full for the exchanges, although the Labour benches were crowded.
Mr and Mrs Lawrence, who sat in the Commons public gallery, occasionally exchanged words but showed little emotion throughout.
Chris Mullin, Labour MP for Sunderland South and chairman of the Home Affairs Select Committee, echoed Sir Norman's concerns, stressing this was not the "moment to declare open season on the police but the moment to make sure serious lessons are learnt".
Mistakes should be owned up to and not covered up, misbehaviour by police should be punished and "the best way to end canteen culture is to spend more time outside the canteen".
Alan Beith, for the Liberal Democrats, said the report told an "horrific story of incompetence, bad management and ignorant racial stereotyping", which ensured that those guilty of racially motivated attacks escaped justice.
Britain had a proud tradition of "policing by consent" but the report had shown a "failure to establish that consent in minority communities".
He also urged Mr Straw, who said there would be a full day's debate on the report, to accept Sir William's recommendation that serious complaints against the police should be investigated by an independent body, and not another constabulary.
Clive Efford, the Labour MP in whose Eltham constituency Stephen Lawrence was murdered, said the publication of the report offered the opportunity for all MPs to "unite", go back to their constituencies and "play a leading role" in tackling racism.
Humfrey Malins, the Tory MP for Woking, argued that institutional racism, unlike a definition of racism in the Oxford Dictionary, could include "accidental conduct". He said that 99 per cent of London's police passed the deliberate racism test "with flying colours".
Peter Bottomley, Tory MP for Worthing West, paid tribute to Duwayne Brooks, Stephen's friend who was with him on the day he was stabbed.
Much of the media coverage of Mr Brooks' involvement in the subsequent investigation had been "adverse - and quite wrong", he said.
Joan Ruddock, Labour MP for Lewisham Deptford and former minister for women, added: "There is a great sense of relief amongst my constituents, a third of whom are black, that at last institutional racism within the Met has been accepted by this House."
Keith Vaz, Labour MP for Leicester East, said the report was "shocking" and that it reflected tragically on the vulnerable situation of the black and Asian community.Reuse content