In her resignation speech, Mrs May mentioned setting up an independent public inquiry into the Grenfell Tower tragedy - in which 72 people died - "to search for the truth, so nothing like it can ever happen again, and so the people who lost their lives that night are never forgotten".

However, this part of speech has drawn criticism from the Fire Brigades Union.

BBC News Channel

Labour MP Rupa Huq said she had sympathy for Theresa May as a "human being".

But Ms Huq added: "She promised that she would fight these burning injustices, but they're un-extinguished all over the place."

Meanwhile Jonathan Bartley, co-leader of the Green Party, said Mrs May was "dealt a terrible hand clearly, but then she proceeded to pour petrol on it and put a match to it.

"She really has not done a good job."

The World at One
BBC Radio 4

Image source, UK Parliament

Labour Party chairman Ian Lavery says it is "outrageous" that the public won't be able to vote for the next prime minister.

"It is simply not good enough to have this decided by a small minority of Conservative members," he says.

"The people in this country deserve the right to put a cross on the ballot paper at a general election."

BBC Radio 5 Live

BBC Radio 5 Live reporter Stephen Chittenden is in Theresa May's constituency of Maidenhead, speaking to people about today's announcement.

Kate said: "I think she's really come to the end of what she was going to try and do.

"It didn't work out for her, I feel quite sorry for her. I think she's been up against a rock and a hard place, and had very little support.

"I think the time is right - who knows what is going to happen next, it's a complete and utter mess really.

"It was one of those things I feel that was never really going to work...

"The self-serving attitudes of politicians these days is not conducive to getting a proper outcome for anything."

Anthony runs a fruit and veg stall.

He said: "I feel sorry for her, she had a really hard run, it was a battle right from day one when [David] Cameron left.

"I think in the end she got into a complete muddle... everyone was telling her to do this, do that - she couldn't be her own person.

"She seems very popular, all our customers seem to like her."

Click to listen live.

Have your say: @bbc5live, external

BBC News Channel

Conservative MP Daniel Kawczynski, who previously voted against Mrs May's deal, said he is "not surprised" that Brexiteer Boris Johnson is currently the frontrunner in the leadership contest.

The MP for Shrewsbury and Atcham said: "Listening to my members in Shrewsbury, he [Mr Johnson] appears to be the preferred candidate amongst them but I will be meeting with my local members to discuss this further."

He added that despite Mr Johnson's sometimes blustering image, he is "now becoming a statesman... he's maturing".

Katya Adler
Europe Editor

Theresa May's resignation was met by EU leaders with expressions of respect rather than regret.

The whole Brexit process is something EU leaders are absolutely fed up with.

The EU has been thinking for a long time about the possibility of Prime Minister Boris Johnson.

They fear that he or another arch Brexiteer will put pressure on getting a new deal by getting in the way of passing a new EU budget.

Image source, EPA

Transport Secretary Chris Grayling - who campaigned to leave the EU in 2016 but has broadly supported the PM and consistently voted for her Brexit deal - has paid tribute to Mrs May.

He said: "The prime minister's statement this morning was incredibly dignified.

"No-one could have worked harder than she has.

"I wish her all the very best for the future."

Will we see other cabinet members follow suit today?

"The Conservative Party has not behaved well," says Charles Walker, an MP in the party.

Mr Walker is vice-chair of the 1922 committee - which represents backbench Tory MPs - and will be part of organising the leadership contest.

"It will be a big challenge for all of us to be optimistic and engage with people," he says.

Mr Walker said a lot of people had asked if the committee's chairman, Graham Brady, would consider standing in the Tory party leadership contest.

"Being an honourable person, he has recused himself from being the chair of the 1922 committee to reflect on that and reflect on his future."

Environment Secretary Michael Gove has paid tribute to Theresa May as a "dedicated public servant".

Asked whether he would run to replace her, he sidestepped the question: "We ultimately need to acknowledge that this is the prime minister’s day.

"I think that she’s put her heart and soul to do the best for this country, at a difficult, challenging, time in Parliament.

"I want to thank her for her service and think we should spend time today giving her the gratitude that she deserves."

The World at One
BBC Radio 4

Image source, PA

Former Brexit Secretary David Davis criticises the Brexit negotiation process, saying "all the compromises were made by the British government".

"The whole of Whitehall has got something to answer," he says, adding "so does the Cabinet".

He criticises members of the Cabinet "who thought it was OK to write in a paper that the government policy was unacceptable", and specifically name checks Amber Rudd and David Gauke, who both backed Remain in the EU referendum.

On Theresa May he says she is "she is a very good lady", but adds "I think this particular problem overwhelmed her".

Image source, Getty Images

Theresa May will not stand down as an MP when she leaves 10 Downing Street next month, her constituency chairman has confirmed.

The PM rang Richard Kellaway on Friday morning before her resignation statement.

"The main concern for us as her association is that she's not going to resign her seat. She will carry on as a Member of Parliament, which is welcomed by us," Mr Kellaway told the Press Association.

"As the prime minister, she could go to the House of Lords if she wants to go that route and carry on, or she could stay a member of Parliament.

"Quite clearly, it's a very troubling and difficult time for her and she'll need to settle down and see what she wants to do."

The BBC takes a look back at Theresa May's career, from her election as an MP in 1997 to her struggles to get her Brexit deal through Parliament and the end of her time as PM.

There hasn't been much praise for Theresa May from her colleagues recently, but today Conservatives have been lining up to pay tribute to their outgoing leader.

Here are a few more MPs who have reacted on Twitter to her resignation announcement.

BBC Politics Live
BBC2's lunchtime political programme

BBC political editor Laura Kuenssberg delivers her verdict on Mrs May's time in office, "if you were writing Theresa May, the chapter, today".

BBC Parliament will tonight be airing key moments and speeches from Theresa May's time in office.

18:00 BST: Her first speech as prime minister

18:05: The Lancaster House speech in which she set out the government's negotiating strategy for Brexit

19:00: Theresa May's statement to MPs on her Brexit deal from November 2017

19:30: Highlights of the debate on Theresa May's EU (Withdrawal) Agreement which resulted in the largest defeat for a sitting government in history

20:00: Theresa May's statement to the Commons on what she described as a "bold new offer” for withdrawing from the EU

21:30: Her resignation announcement

Image source, EPA

A spokeswoman for Emmanuel Macron has said the French president sent Theresa May a message of support following her resignation.

The spokeswoman said: "The prime minister of Britain has announced she will shortly quit her role.

"She has led a courageous effort to make Brexit happen. She worked towards Brexit in the interests of her country and in respect of her European partners.

"The president has sent her a personal message of support and thanks.

"It is now the work of the United Kingdom, following its procedures, to appoint a new prime minister.

"France holds itself ready to work together with the new British prime minister on bilateral and European issues. Our relationship with the United Kingdom is essential in all areas. It is too early to speculate on the consequences of this decision."

Image source, AFP/Getty Images

Trade Secretary Liam Fox has praised the prime minister, saying he believes she acted with grace, dignity and honour.

Speaking at Strathclyde University in Glasgow he said the Conservative Party would "not be short of talent" to replace her as leader, and did not quite rule out running himself, saying "stranger things have happened - but not much stranger".