The Prime Minister has invited SNP leader Nicola Sturgeon for crisis talks on the Union after the First Minister warned he would be standing in the way of democracy if he denies Scotland a second independence referendum.

The SNP fell one seat short of an overall majority in the Scottish parliament elections, securing 64 seats, but the final result still leaves Holyrood with a pro-independence majority.

In her victory speech, Ms Sturgeon told supporters the result proved a second independence vote was the “will of the country” and said any Westminster politician who stood in the way was “picking a fight with the democratic wishes of the Scottish people”.

But Boris Johnson, in a letter to Ms Sturgeon, argued the UK was “best served when we work together” and called for a conversation about “our shared challenges” in recovering from the pandemic.

In a letter shared by No 10, the Prime Minister congratulated Ms Sturgeon on her re-election and said: “I would like to invite you to join me, UK Government colleagues and others at a summit meeting to discuss our shared challenges and how we can work together in the coming months and years to overcome them.

“We will all have our own perspectives and ideas – and we will not always agree – but I am confident that by learning from each other we will be able to build back better, in the interests of the people we serve.”

Communities Secretary Robert Jenrick stressed that, despite the strong preference in Scotland for pro-independence parties, it would be a “grave error” to pursue another border poll.

The Cabinet minister told BBC News: “I don’t know what the future might hold but our sole focus right now must be on recovery, and I think being distracted in any way by talk of constitutional wrangles would be a grave error.”

The dispute over a follow-up referendum came as Labour recriminations began over its poor showing in the Super Thursday elections on Thursday.

Deputy Labour leader Angela Rayner was sacked on Saturday from her role as chairman and national campaign coordinator.

It comes after the Opposition outfit lost the Hartlepool by-election – with the North East town voting for a Tory MP for the first time in 60 years – and incurring a net loss of six councils and more than 200 seats in the local elections as voters in its traditional heartlands deserted the party.

Prominent figures on the left of the party hit out at the move, with former shadow chancellor John McDonnell calling it a “cowardly avoidance of responsibility” by leader Sir Keir Starmer.

The row came despite Labour faring better in Saturday’s results, producing surprise victories in the West of England and Cambridgeshire and Peterborough mayoral contests, while comfortably winning second terms in Greater Manchester and the Liverpool City Region with Andy Burnham and Steve Rotheram respectively.

Mr Burnham – who has been installed as the bookmakers’ favourite to replace Sir Keir, despite not being an MP – did not close the door on the possibility of becoming the next Labour leader, saying: “In the distant future, if the party were ever to feel it needed me, well, I’m here and they should get in touch.”

In London, Labour’s Sadiq Khan had to wait late into the night to find out that he had won a second term as mayor in City Hall after fending off a challenge from Tory rival Shaun Bailey, and Marvin Rees won a second term as Bristol mayor for Labour, beating Green candidate Sandy Hore-Ruthven in the run-off after the Liberal Democrat and Conservative candidates were eliminated.

Elsewhere in England, The Tories completed their hat-trick of victories to go with their shock Hartlepool by-election win and stomping Tees Valley mayoral victory when Andy Street was re-elected as West Midlands Mayor.

By the close of Saturday, with results in from 129 of 143 English councils, the Tories had a net gain of 11 authorities and more than 280 seats, while Labour had a net loss of six councils and more than 220 seats.

Mr Johnson vowed there would be “no let up in levelling up” after his successful further dismantling of Labour’s so-called “red wall”, adding: “Voters have put their trust in Conservative representatives, councillors and mayors and we must deliver for them.”

In Wales – as in Scotland and England – the party in power was rewarded by the voters.

Mark Drakeford’s Welsh Labour avoided the kind of electoral drubbing Sir Keir endured on Friday.

With the final declarations made on Saturday, Labour ended with exactly half the 60 seats in the Senedd – one short of an overall majority – equalling its best ever results.

First Minister Mr Drakeford, who extended the majority for his Cardiff West seat by more than 10,000 votes, vowed to be “radical” and “ambitious” in government.