BBC director general Tim Davie said an independent review of BBC social media guidelines would be carried out - and denied the BBC had backed down.

Prime Minister Rishi Sunak said "it was right" the matter had been resolved.

But on Monday the BBC continued to face criticism from a range of sides.

Lineker said he supported the review and looked forward to getting back on air, describing the last few days as "surreal" and thanking people for their "incredible support".

But Tory backbench MP Philip Davies told the Mail Online the BBC's decision was a "pathetic capitulation" to Lineker and the "start of the end for the licence fee", while ex-cabinet minister Jacob Rees-Mogg also warned the "licence fee has passed its sell-by date".

Labour's shadow culture secretary Lucy Powell, meanwhile, said the return of Lineker was welcome, but "much bigger questions remain about the impartiality and independence of the BBC from government pressures".

Former BBC director-general Greg Dyke compared the row to "like a 5-0" win for Lineker and said he thought there was a public perception the government had bullied the broadcaster into removing the TV star, which was "very bad news" for the BBC.

Ex-BBC News executive Sir Craig Oliver, who went on to be a Downing Street communications chief under then-Prime Minister David Cameron, described the situation as "a total mess" and said it was the "wrong choice" to have asked Lineker to step back in the first place.

"The reality is the BBC today has announced it will have a review of its social media guidelines," he told the BBC. "In fact, it needs a review of how it handles crisis like these."

Sir Michael Lyons, a former BBC chairman under Labour, told BBC Newsnight: "It simply isn't possible for the BBC to be a champion of dissent in Russia and Hong Kong, and at the same time not leave space for dissent in this country."

He added there was "a big question about consistency in the way rules are applied" saying some BBC stars have been allowed to say things about the Labour Party, referring to a tweet by Lord Alan Sugar advising people not to vote for Jeremy Corbyn.

Former controller of BBC editorial policy Richard Ayre said rewriting guidelines was not straightforward and was "going to be a nightmare".

"Whatever emerges will be unsatisfactory to a significant number of people. It's inevitable."

Earlier, Davie insisted the decision to pull Lineker off air was about buying some time until the two sides could come to an agreement over his political tweets - and said that was exactly what had happened.

He said he took "proportionate action", adding: "We believe we did the right thing. I think I did the right thing."

When challenged by BBC media correspondent David Sillito on whether it was a climbdown by the BBC, he said: "I don't think so.

"I've always said, we needed to take proportionate action. For some people, by the way, we've taken too severe action... others think we're being too lenient."

In a separate statement on Monday, Davie apologised, saying: "Everyone recognises this has been a difficult period for staff, contributors, presenters and, most importantly, our audiences. I apologise for this."

The row began last week when, in a tweet, Lineker said the government's new Illegal Migration Bill was an "immeasurably cruel policy" and said the language used around it was "not dissimilar to that used by Germany in the 30s".

His words were criticised by Conservative ministers, including the home secretary.

Lineker was told on Friday to step back from presenting Match of the Day until an agreement was reached. It triggered an unprecedented wave of walkouts from fellow pundits and commentators in solidarity with Lineker, which disrupted weekend football coverage across the BBC.

Sports presenter Mark Chapman - who did not present BBC Radio 5 Live's Saturday Coverage or Match of the Day 2 on Sunday on TV - returned to football radio show The Monday Night Club and apologised for the lack of service over the weekend.

He said it had been "miserable and difficult" for the staff involved and it was "disgusting and unfair" that the staff who did work on the weekend received abuse.

He added: "It is ironic in a row over impartiality we have all been seen to be taking sides, and I feel there are lessons to be learned by all involved."

BBC Scotland also had full coverage of Monday evening's Scottish cup tie between Falkirk and Ayr United after its programming was also limited over the weekend.

After his return to BBC TV was announced, Lineker tweeted: "However difficult the last few days have been, it simply doesn't compare to having to flee your home from persecution or war to seek refuge in a land far away.

"It's heartwarming to have seen the empathy towards their plight from so many of you. We remain a country of predominantly tolerant, welcoming and generous people."

The government's Illegal Migration Bill passed its first hurdle in the Commons by 312 votes to 250 on Monday night, with the majority of Tory MPs voting for the plans.

'Abide by the guidelines'

Lineker has hosted Match of the Day since 1999 and is the BBC's highest paid star, having earned about £1.35m in 2020-21. He is employed by the BBC on a freelance basis.

BBC employees are expected to remain impartial on political matters and must follow strict social media guidelines, but there is significant debate about how they should apply to staff outside of news.

Lineker said he backed the independent social media review which Davie said will have a "particular focus" on how the guidelines apply to freelancers outside news and current affairs.

"Shortly, the BBC will announce who will conduct that review," Davie said. "Between now and when the review reports Gary will abide by the editorial guidelines, that's where we are."

Lineker is expected to return to host Match of the Day's live coverage of the FA Cup quarter-final between Manchester City and Burnley on Saturday evening.

He is then set to front Sunday's live coverage of Grimsby Town at Brighton & Hove Albion on BBC One.

The row over Lineker's tweets also renewed questions over BBC chairman Richard Sharp. A review into Mr Sharp's appointment as BBC chairman is investigating whether he failed to properly disclose details of his involvement in the facilitation of an £800,000 loan guarantee for the then-prime minister Boris Johnson. He has denied any involvement in the arrangement of a loan for Mr Johnson.

Asked about Mr Sharp, Mr Sunak told the BBC: "He was appointed before I was prime minister through an independent process. And that process is also now being reviewed independently. It's right that we let that review complete."

Liberal Democrat leader Sir Ed Davey tweeted: "The BBC has made the right decision on Gary Lineker - now it's time for Rishi Sunak to do the right thing and sack Richard Sharp. The BBC needs a proper independent chair not a Johnson acolyte."

Labour leader Sir Keir Starmer said Mr Sharp's position was "increasingly untenable".