But the head of Scotland Yard indicated that he is extremely unlikely to stand down if, as expected, it is members of his force who are condemned for the way they investigated the murder of the black teenager along with more sweeping condemnation of racist attitudes in the Met.
The most senior police officer in Britain, in an interview with The Independent, also called for a new national anti- racism strategy to cover not just the police service, but schools, health and benefit agencies. The Home Office is understood to be in discussion with the Met on drawing up plans for changes to race-relation legislation and training.
Sir Paul, who apologised on Thursday to Stephen's parents at a heated public session of the Lawrence inquiry for failing to the catch their son's killers said - for the first time - that he believed the murder inquiry is a resigning issue. "If at any stage anyone suggests that I've acted dishonourably or dishonestly ... then for me there's no question you should go."
He added: "I have acted totally honourably and sincerely in trying to take this issue forward ... If the inquiry was saying that I personally had somehow done something wrong in relation to this case then clearly I would be deeply distressed."
His comments come as the inquiry into the racist stabbing to death of Stephen, 18, at a bus stop in south-east London in 1993, draws to a close. The teenager's parents, Doreen and Neville, have both called for the resignation of Sir Paul, who took over the Met two months before their son was murdered. Mrs Lawrence said on Thursday: "For five years we have still not been given justice ... he should resign."
But Sir Paul said yesterday that he saw a distinction between personal criticism of his role and wider criticism of the Met and individual officers.
He said that in the past 24 hours he had received messages from "key people in the minority ethnic community in London who have said they admire what I'm doing."
"When the inquiry comes out I have to make a personal decision. Do I go with those who say you understand this issue, you have done a great deal, things have gone wrong, but we want you to see things forward. Or [do I go with] the understandable passion and grief felt by Mr and Mrs Lawrence ... " He added: "People have been saying `please stay on and see this through, however ... painful it is'.
"There's this sort of greyer area around the balance between moving the service forward and knowing what needs to be done and hearing the pain from the black community and almost a desire for a fresh start," he said.
He argued that he gave a top priority to tackling racism within the police and feels "passionately" about the issue. "My ambition is that at some stage people will be able to say `Yes, that was a tragic case, but something good has come out of it'," he said. "If all that comes out of this tragedy is a quick fix, lay it at the door of the Met, or [what is seen as] the police-service notions of racism, tragically that will not move the debate forward. It certainly will not move forward the challenge of racism in society generally."
To the anger of supporters of the Lawrence family, Sir Paul has refused to accept that the Met was infected with "institutional racism".
However, he argued yesterday that there needs to be a nationwide anti- racism programme for all areas of the public sector. He said this should include recruitment practice and how powers are used in "police, health, social services, benefits [agencies] and education".
He said it was important to look at whether racism was being involving in stop and search, arrests, social security benefits, and the treatment of patients in the health service.
"There should be [a requirement] for all public services to have a demonstrable and compelling programme at every level to avoid racism occurring ... " He added: "What certainly is going to come out of [the Lawrence inquiry] is ministerial support for greater effort for dealing with racial crime and racial incidents."Reuse content