Two in five Londoners are less likely to trust the Metropolitan Police following claims that undercover officers spied on Stephen Lawrence's family, a BBC London survey indicates.
A ComRes poll of 1,000 Londoners suggested a quarter believe the Met is institutionally racist, including 38% of black and minority ethnic people.
A quarter also believed there was widespread corruption.
But 85% of those polled said they trusted the Met overall.
Met Commissioner Sir Bernard Hogan-Howe told Vanessa Feltz on BBC London 94.9: "It is a challenging set of statistics. It's not pleasant hearing.
"I was shocked by the claims so I have no doubt the rest of London was shocked, so I understand why people very shortly after those revelations reacted in that way."
In a Guardian and Channel 4 Dispatches report on 24 June, Peter Francis, a former undercover police officer, claimed he was ordered to infiltrate the Stephen Lawrence campaign in 1993.
He said it was a hunt for "disinformation" to use against those criticising the police.
Sir Bernard said the force needed to get to the bottom of these allegations, which are being investigated, and added: "I hope it doesn't destroy the great work the Met's doing everyday of the year."
Asked to what extent the revelation had affected people's opinion of the Met, 37% told ComRes they were less likely to trust the force.
Twenty-seven percent said they believed the Met was "institutionally racist" - an assessment made in the 1999 Macpherson report into the investigation of the murder of Stephen Lawrence.
Twenty-four percent of respondents said they believed there was widespread corruption in the Met, including more than a third, 36%, of black and minority ethnic (BME) Londoners.
Although overall people said they had trust in the force, the percentage distrusting the Met rose significantly among ethnic minorities, with a quarter of black Londoners, 24%, and 15% of all BME people saying they thought the Met was untrustworthy.
This compared with only 9% of white Londoners.
Sir Bernard said: "I think in this particular survey after that shocking allegations it's probably not shocking that people have still got their concerns.
"I have said all along that I hope we are not institutionally racist and there's good evidence we are not but there's some evidence we may be."
The Met's police and civilian staff are representative of London, he said, adding one in three PCSOs are from minority background, and the figure stands at one in four for police staff as well as special constables.
He said 3,000 police officers, about 10%, are from the BME background, compared to 300 in 1993.
Stop and search operations have also come down from about 500,000 to 350,000 over the last two years, with complaints falling to 900 - a 50% drop, the commissioner said.
Over the past year the Met faced 11 allegations of racist behaviour by officers and the force has taken "severe actions" by sacking six officers.
"We aren't yet perfect, no organisation I don't think in this country is perfect in terms of things like institutional racism, but we have moved a long way," Sir Bernard added.
Stephen Lawrence was 18 when he was stabbed to death by a gang of white youths as he waited at a bus stop in south-east London.
It took 18 years for Gary Dobson and David Norris to be convicted of his racist murder.
Appearing before the London Assembly's Police and Crime Committee last Thursday, Sir Bernard said he was "shocked" by Mr Francis's claims and acknowledged it was "profoundly damaging" to public confidence.
Len Duvall, Labour, Co-operative Member of the London Assembly for Greenwich and Lewisham, said the incidents raised issues in confidence in the management and supervision of the Met.
Doreen Lawrence said the claims were like "taking steps back" and that it would take time to get trust in the Met back.
ComRes interviewed 1,000 London adults by telephone between Friday and Tuesday for the poll.
Stephen Lawrence's friend Duwayne Brooks, who was with the teenager the day he was killed, will meet Nick Clegg on Friday to discuss allegations of police misconduct, Mr Brooks's solicitors have said.
The meeting comes after the BBC revealed that the Met had secretly recorded meetings between Mr Brooks and his lawyer.