Pollsters YouGov predicted the Tories would win 359 MPs, a gain of 42, with Labour on 211, a loss of 51.
The SNP are predicted to win eight more seats, putting them on 43, while the Liberal Democrats are set to stall with a gain of just one MP, putting them on 13.
Two years ago, the polling company was criticised after it predicted that Theresa May’s Tories would fail to win a majority despite being in the lead.
But there was an immediate warning from Mr Johnson’s top Downing Street adviser, Dominic Cummings, who made his first intervention in the election campaign to insist that the contest was “much tighter” than it seems.
Mr Cummings used a blog post hours before YouGov’s announcement to send up what he called a “bat signal” to Brexiteers, telling them not to be complacent about the election result.
YouGov’s multilevel regression and post-stratification (MRP) analysis used data from 100,000 interviews with voters over the past seven days to predict the result in constituencies across Great Britain.
The findings suggest that the ‘red wall’ of seats in the Midlands and north of England will crumble, with the Tories making gains across traditional Labour heartlands.
In Scotland, despite predictions of a Scottish Tory wipeout, the SNP are expected to take just two seats from the Conservatives, ousting Stephen Kerr in Stirling and Paul Masterton in East Renfrewshire.
Labour are predicted to lose all but two of their Scottish seats: Ian Murray’s Edinburgh South, and Hugh Gaffney’s Coatbridge, Chryston & Bellshill.
YouGov’s figures have the Liberal Democrats losing the seat of Caithness, Sutherland & Easter Ross and failing to take the UK’s most marginal constituency, North East Fife.
SNP 'set to do well'
Chris Curtis, the Political Research Manager at YouGov said: “The SNP are set to do well in Scotland but still fall short of their performance in 2015.
“Most of their gains are coming at the expense of Labour who are losing five of their seven seats they won back in 2017.
“The race in many Conservative-held constituencies is tighter, but the Tories are holding onto 11 of their 13 seats as things stand.
“Two of the four Lib Dem-held seats look set to be close tussles with the SNP, but Jo Swinson should hold East Dunbartonshire.”
YouGov’s findings were rejected by Mr Johnson’s top strategist, who said there was still a “very real possibility” of a hung parliament despite the Conservative Party maintaining a significant lead over Labour.
Mr Cummings - who is credited with masterminding the successful Vote Leave campaign in the 2016 referendum - said that voting for Nigel Farage's Brexit Party in key Conservative target seats in the Midlands and the North of England risked handing victory to Labour.
He warned if there is no Tory majority, the Labour and the SNP would combine to "cheat" a second Brexit referendum by giving the vote to EU nationals in order to secure a Remain vote.Cummings also appeared to undermine one of the central claims of the Tory campaign - that Labour and the SNP would hold two referendums next year, on Brexit and Scottish independence - by initially writing that indyref2 would take place in 2021.
The blog post was quickly edited to read: “And there’ll be another Scottish referendum.”
Mr Cummings is not thought to be playing a direct role in the Tory campaign, and was reported to be taking time out to undergo surgery.
However, it is understood he stood down from his position as a special adviser in Number 10 when parliament was dissolved - as aides are required to do before joining an election campaign.
“If Boris doesn’t get a majority, then Corbyn and Sturgeon will control the government,” he wrote.
“Their official policy is to give the vote to millions of foreign citizens to cheat their second referendum.”
Cummings went on: "You will see many polls in the coming days. Some will say Boris will win," he wrote."Trust me, as someone who has worked on lots of campaigns, things are MUCH tighter than they seem and there is a very real possibility of a hung parliament."Without a majority, the nightmare continues. ALL other MPs will gang together to stop Brexit and give EU citizens the vote. It's that simple."
Another MRP exercise carried out by polling company Focaldata for the Best for Britain campaign, which is seeking a second EU referendum, suggested the Tories could secure a 366-seat majority unless Remain supporters vote tactically.
However, Best for Britain said the findings suggest that fewer than 120,000 voters across the UK casting their ballots tactically to deny the Conservatives a majority.
Focaldata examined polling responses from 39,476 voters between 15 October and 24 November.
In the 57 target seats identified by Best for Britain as the places where tactical voting has the best chance of ousting Conservative MPs, just 4,000 votes would have to be cast tactically to reduce the Tory numbers in the Commons to 309. The list includes seven Tory constituencies in Scotland.