Zack Polanski has seen his popularity slump amid a backlash at his criticism of police over the Golders Green attack.
The Green leader's personal ratings have tumbled 14 points over the past week, leaving him with a net score of minus 27.
The research by More in Common suggests that Mr Polanski's clashes with the Scotland Yard commissioner might have harmed his standing.
Labour has also been targeting the Greens heavily in campaigning for the local elections, highlighting alleged 'disturbing' views held by some candidates.
Keir Starmer is desperately trying to hold back a Green surge amid fears that the party is poised to make big gains on Thursday, especially in London and the North West.
Zack Polanski has seen his popularity slump amid a backlash at his criticism of police over the Golders Green attack
The research by More in Common suggests that Mr Polanski's clashes with the Scotland Yard commissioner might have harmed his standing
The latest poll, conducted between May 1 and yesterday, suggests Mr Polanski is still performing better than Sir Keir, who has a dire rating of minus 45.
However, he is significantly less popular than Kemi Badenoch, Ed Davey and Nigel Farage.
Luke Tryl of More in Common said: 'Looking at the numbers it's both a rise in negatives and a fall in positives, in particular more young people seem to have shifted from ''good job'' to ''neither good nor bad job''.
'So a mix of more disapproval and more uncertainty.'
The Green Party leader was condemned last week for endorsing claims on social media that Metropolitan Police officers were heavy-handed after three people were stabbed, earning a public rebuke from Commissioner Sir Mark Rowley.
He faced barbs from within his own ranks, as well as from Sir Keir who branded him 'disgraceful' and 'not fit to lead any political party'.
Mr Polanski issued a half-hearted apology on Friday night, but in a round of media interviews on Sunday doubled down on questioning the police's actions.
He told the BBC's Sunday with Laura Kuenssberg he was 'concerned by what he saw and remains concerned' by videos of the arrest last Wednesday.
He went on: 'I think it's important to say that officers are incredibly brave when they run towards situations that most of us, including myself, would want to run away from.
'I also accepted, as an elected member of the London Assembly and in fact the Police and Crime Committee, that it's important that everyone who works in public service, including people who are being brave, should not be above scrutiny.
'And so I think it's important that I have that conversation with the Commissioner and we always make sure that action is proportionate, no matter how brave.'
He also criticised Sir Mark for intervening publicly, saying: 'Open letters aren't an appropriate way to do politics either in a local election.'
Mr Polanski also defended pro-Palestinian marches through London saying they do not make British Jews any more 'unsafe'.