Asked to rate the performance of British prime ministers since 1945, some 49% of people told pollster Ipsos that Mr Johnson had done a bad job during his time in Downing Street.
The figure was worse than those for both his immediate predecessors. Some 41% of people thought Theresa May had done a bad job, the second highest total, while David Cameron’s 38% was the third highest total.
While Mr Johnson may have had the highest number of people saying he had done a bad job, he also had the fourth-highest number telling Ipsos he had done well.
Some 33% of the 1,100 people surveyed by Ipsos said he had done a good job in office, behind Tony Blair on 36%, and Margaret Thatcher on 43%.
Mr Johnson’s political hero Winston Churchill came top out of the post-war prime ministers, with 62% saying he had done a good job.
Keiran Pedley, director of political research at Ipsos, said: “Winston Churchill continues to top our list of prime ministers the public think did a good job in office, followed by Margaret Thatcher.
“Boris Johnson will be reasonably content with finishing 4th on that list but less happy about topping the list for having done a bad job.”
Mr Johnson, who is currently on a farewell tour of the country before he leaves office on Tuesday, was also one of the few post-war prime ministers to have more people say he had done a bad job than a good one.
His net rating in the Ipsos poll, which was carried out between August 19 and 22, was -16. David Cameron, on -8, and Theresa May, on -13, were the only others to have a negative net rating.
Mr Pedley added: “However, there is a certain degree of recency bias in who tops the bad job list, with Johnson making up a top three with Theresa May and David Cameron.
“Time will tell how Johnson’s legacy is judged, as we see by improved scores for Gordon Brown over time, negative perceptions today may soften in the future.”
The number of people telling Ipsos that Gordon Brown did a good job rose from 24% in February 2021 to 31% in August 2022 while the number saying he did a bad job fell from 37% to 31%.
Other recent prime ministers including David Cameron, Theresa May and John Major also saw their scores improve.