And support for leaving the UK is now neck and neck with backing for the union among Scots, according to a new poll for the Sunday Times.
The narrowing gap on the constitutional issue comes as Nicola Sturgeon seeks to hold a second referendum on leaving the UK late next year. The Panelbase survey of 1,024 voters shows that 49 per cent of those questioned support Scottish independence (up one point since last month) while 51 per cent are against it.
However, when asked how they would vote if Johnson were to become prime minister, 53 per cent say they would back independence, with 47 per cent against it.
SNP depute leader Keith Brown said: "This is a stunning poll that shows independence is within touching distance.
"Even without the nightmare scenario of Boris Johnson as Prime Minister a referendum would be too close to call - but if he wins, as expected, backing for independence is set to surge.
"Under any leadership, the Tories' support is slumping in Scotland - and after coming fourth in the European election the party is now set to lose seats at both Holyrood and Westminster.
"While we take nothing for granted, it's no wonder voters are continuing to put their faith in the SNP - the only party with a way out of the Brexit mess and a vision for a better Scotland."
The poll found that Johnson has a personal approval rating of minus 37 north of the border, behind his leadership rival Jeremy Hunt, who shares an approval rating of minus 24 with Brexit Party leader Nigel Farage.
First Minister Nicola Sturgeon's rating is neutral while Scottish Conservative leader Ruth Davidson is on minus one.
A Scottish Conservative Party spokesman said: "No matter who wins the leadership race, Scotland is better off remaining part of the UK.
"There is no evidence the Scottish public have the appetite for a re-run of the 2014 vote.
"It is time instead for us to come together, to move on from constitutional division and focus on the things that matter."