Boris Johnson plans to bring his Brexit deal back to parliament next week, as his Conservative party was predicted to have its best general election result since 1987 after more than nine years in government.

With Thursday night’s exit poll putting the Tories on course for an 86-seat majority, the prime minister intends to push ahead with his election pledge to have MPs vote on his withdrawal agreement by Christmas, and for the UK to leave the EU by the end of January.

If the exit poll is correct, parliament is set to return on Tuesday with a Conservative government, which will move the second reading of the withdrawal agreement bill next Friday, 20 December. Johnson has insisted he is able to negotiate a post-Brexit trade deal with the EU without the need to extend the transition period beyond the end of 2020.

UK general election 2019: exit poll predicts 86-seat Tory landslide majority – live news Read more

Speaking at the count for his constituency of Uxbridge and South Ruislip, Johnson said: “This one-nation Conservative government has been given a powerful new mandate to get Brexit done – and not just to get Brexit done but to unite this country and to take it forward.”

The cabinet minister Michael Gove said Johnson had been clear he would use his mandate to make sure the withdrawal agreement was completed by 31 January and would then move “quickly and expeditiously to secure a new arrangement with the EU based on free trade and friendly cooperation”.

He dismissed the idea that 11 months was too short a time for such a complex negotiation. “A long time ago I was a reporter,” he told Sky News. “Deadlines concentrate minds.”

The chancellor, Sajid Javid, told the BBC that a majority Conservative government would arrange “the smoothest of all exits from the EU, while the foreign secretary, Dominic Raab, told Sky News it would be much easier to negotiate a free-trade deal with the EU with a majority.

“If we’ve got the kind of majority that is suggested, this will very much strengthen and reinforce our position in phase two,” he said. Raab – who retook his Surrey seat of Esher and Walton, despite rumours he could lose – said it would also be easier for the EU as it would have a negotiating partner that was “much more predictable”.

The European council president, Charles Michel, said EU leaders would discuss the results of the election on Friday, but that there was “a strong message” coming from the UK. “We will see if it’s possible for the British parliament to accept the withdrawal agreement to take a decision, and if it is the case, we are ready for the next steps.”

The former Conservative chancellor George Osborne – historically a critic of Brexit and Johnson – responded to the exit poll by declaring the UK was “entering the Boris Johnson era of British politics”.

He said Johnson had won by uniting the leave vote and splintering the remain vote. “Something has become immediately apparent – we’re leaving the European Union. Brexit is settled, at least the initial phase. We will leave the European Union in the coming weeks.”

The first shock result of the night came in Blyth Valley in Northumberland, held by Labour since its creation in 1950, which fell to the Tories by 712 votes. Labour won the seat by 7,915 votes in 2017. By 3am, the Conservatives had continued to take previously safe Labour seats like Workington in Cumbria, Darlington in county Durham and Leigh in Greater Manchester.

Senior Tories took to the airwaves to say the poll confirmed what they had found campaigning across the country.

Raab said he had not been unduly worried during the campaign. “There are two debates and two theatres in most general elections,” he said. “There’s the media theatre – the punditry and the social media and all that – and then there’s the steady feedback you get, the quiet moments you get with swing voters on the doorstep.

“It was very striking. I was up in Wolverhampton and I was up in Warrington and we are clearly getting a hearing in homes across the country where we haven’t done for some time. Part of that was about Brexit and part of that, I think, was about the positivity that the prime minister and the Conservatives have offered.”

James Cleverly, the Conservative party chairman, said: “I spent much of this week, over the weekend, zigzagging across the Midlands and the north of England, and in long-standing Labour-held constituencies there was fury. I mean not anger, fury, at both the Labour party and Jeremy Corbyn.

“A lot of people felt they were lied to in 2017 when the Labour candidates looked them in the eye and said ‘I will deliver Brexit’. [They] then spent the next two and a half years trying to prevent it.”

Ruth Davidson, who stood down as leader of the Scottish Conservatives partly due to the national party’s Brexit stance, said Johnson had had a mixed response on the doorstep in Scotland, with middle-class remainers “not taking to him” but “aspirational working class, particularly men, [thinking] he’s great”.