The survey conducted among 2,114 adults from August 5-6 found that 49% of respondents believed that Starmer was handling the situation badly, versus 31% who said he was dealing with the riots well.
Seven in 10 respondents said the majority of rioters would evade punishment, while only 22% said they were confident that at least most of them would be held accountable.
Far-right protesters rallied against the influx of migrants across the country after unconfirmed reports suggested the perpetrator in the deadly stabbing attack on a children's dance club in Southport was a refugee. The attacker was later identified as a Welsh-born boy of Rwandan descent.
The attack occurred on July 29, resulting in the deaths of three children and injuries to several others. Police arrested the 17-year-old boy and charged him with three counts of murder and 10 counts of attempted murder. The attack is not being treated as an act of terrorism.