The Labour labour fared better than the prime minister when it came to competency in data taken from 13-15 June.
At 41%, Johnson is down 14% since April while Sir Keir is currently on 45%, up 14% in the same period.
Only 11% of people saw the opposition leader as incompetent (as many are still yet to form a view) but a considerable 47% believed the PM was.
Despite Johnson’s perceived incompetence, 41% of Britons think a Conservative government led by him would be better at managing the economy, compared to just 21% who would prefer Sir Keir.
That is good news for the Tory leader because the country now sees the economy as the most important issue (61%) following the coronavirus lockdown.
The respondents selected the economy ahead of healthcare (60%) and Brexit (45%).
Johnson again clashed with Sir Keir at prime minister’s questions (PMQs) on Wednesday.
The two argued over child poverty after the government performed a U-turn and offered free school meals following a campaign from Manchester United striker Marcus Rashford.
Sir Keir welcomed the change of heart but said more needed to be done to combat rising levels of child deprivation.
Johnson later criticised Sir Keir over the return of children to schools, suggesting the opposition and trade unions were hampering efforts to reopen.
The PM said one of the best ways to help the poorest children in the country “would be to encourage all kids who can go back to school to go back to school now, because their schools are safe”.
He repeatedly challenged Sir Keir to say it was safe for children to return and accused the opposition of “wibble-wobble” over the issue.