More than half (55 per cent) of the 1,006 adults polled said they thought the Prime Minister had handled the outbreak “fairly badly” or “very badly”.
Just 30 per cent of respondents said Mr Johnson was doing “fairly well” or “very well”.
In contrast, 82 per cent of those polled said Nicola Sturgeon had handled the crisis “fairly well” or “very well”.
Only eight per cent of Scots think she is doing “fairly badly” or “very badly”, meaning her net approval rating is +74.
The poll was conducted before it was revealed that Mr Johnson’s chief adviser, Dominic Cummings, had taken a trip to Durham while he was self-isolating with coronavirus symptoms.
Despite a high rating for Ms Sturgeon and the Scottish government, the overwhelming proportion of Scots think the country entered lockdown too late.
Just 26 per cent of respondents thought that Scotland had entered the lockdown at the right time, compared to 70 per cent who thought it should have happened sooner.
But a majority of Scots support the Scottish government’s plan to lift coronavirus restrictions at a different time to the rest of the UK.
81 per cent backed the idea that Scotland should ease the lockdown at a different pace “if the Scottish government believes that is necessary.”
Just 19 per cent said they thought all the nations of the UK should list restrictions at the same time.
Writing for the BBC, polling expert Professor John Curtice described the difference in how well the UK and Scottish governments are thought to have handled the coronavirus crisis as "remarkable."
Professor Curtice wrote: “The difference in how well the UK and Scottish governments are thought to have handled the coronavirus crisis is remarkable.
“After all, they have both faced very similar criticisms, including too little PPE, too little testing and too little care and attention to the needs of care homes.
“In part, the explanation lies in long standing differences in attitudes towards the two governments. Ever since the advent of devolution, voters in Scotland have been inclined to evaluate the Scottish government more highly than its counterpart in London, whatever the issue at stake.
“The Scottish government benefits from a halo effect whereby credit for what is done well in Scotland is attributed to Holyrood and blame for poor performance is laid at the door of Westminster.
“Meanwhile many voters will be viewing the two governments through a partisan lens. And it also looks as though the Scottish government is closer to the public mood as to how the lockdown should now be handled,” he said.
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