Mrs May today tearfully announced that she will resign as leader of the Conservatives on June 7, but will remain PM until her successor is found.
North Shropshire MP Owen Paterson has said she has made the right decision to step down as Tory leader.
Mr Paterson, a fierce critic of Mrs May, said: "I think history will look more kindly towards her than contemporary comments.
"She did get the second largest vote in British history, and should be remembered for that.
"She has made the right decision, it's a good thing and we now need to move on. The important thing is delivering the vote of 17.4 million people, and we need to get on with this leadership election so we can do that."
He would not be drawn on who he wanted to see as the next party leader.
"The important thing is we need a leader who is going to deliver Brexit as rapidly as possible," said Mr Paterson.
"We all know who the strong candidates are, they are in the papers every day, but I will reserve judgement until I have heard what they have got to say."
Shrewsbury and Atcham MP Daniel Kawczynski praised Mrs May for the manner of her departure, and regretted that she had been prevented from taking the UK out of the European Union.
"I think she's resigned with great dignity, I wish her every success for the future, and I very much hope she remains in the Commons and continues to take a very active part," he said.
"I do feel a certain regret that extremists – I don't use that word lightly – Brexit and Remain extremists both in the Conservative and Labour Party have caused this gridlock.
"I very much hope in time that the next leader, whoever he or she is, will be able to bang some heads together to get some form of compromise so we can move on."
Mr Kawczynski said he was taking soundings from members of Shrewsbury and Atcham Conservative Association on who the next leader should be. He said it was very important that the final decision rested with party members.
He said at this stage his preference would be one of Boris Johnson, Michael Gove or Jeremy Hunt.
Ludlow MP Philip Dunne said that Mrs May has 'given her all' during her tenure.
"I applaud the dignified speech Prime Minister Theresa May has just made in announcing her resignation as Leader of the Conservatives in two weeks time and as PM once a successor is chosen," he said. "She has given her all in commitment to her country and deserves our respect."
I applaud the dignified speech Prime Minister Theresa May has just made in announcing her resignation as Leader of the Conservatives in two weeks time, and as PM once a successor chosen. She has given her all in commitment to her country and deserves our respect.— Philip Dunne (@Dunne4Ludlow) May 24, 2019
Telford MP Lucy Allan tweeted her support following a statement from Sajid Javid, who said: "Nobody could have worked harder or had a greater sense of public duty than the Prime Minister. Her dedication in taking our country forward had been monumental. She has served her country with fortitude and we are grateful to her for it."
Glyn Davies, MP for Montgomeryshire, had been a loyal supporter of Mrs May .
“I’ve always been very supportive of her, and think she has performed a Herculean effort to secure an agreement, but in the end she had no option but to resign and let someone else see if they can come to an agreement.”
He said the Conservative Party would pay a very heavy price if it could not deliver its promise to ensure Britain left the EU.
Of the potential leaders, Mr Davies said he was a huge admirer of both Michael Gove and Jeremy Hunt, but said there was also a lot of support among the party membership for Boris Johnson.
“I think Boris Johnson will be in the final two, it’s what Conservative Party members want up and down the country,” he added.
Nicola Lowery, chairman of the Telford Conservative Association, paid tribute to the outgoing PM.
She said: “The Prime Minister delivered a very heartfelt, emotional and truly dignified speech. Theresa May has shown tremendous courage and is a devoted public servant that has shown tremendous commitment and tried her best in her devotion and service to her country.
"It is inspiring to see a Prime Minister that clearly cares greatly for her country, has a profound sense of duty and it is with the deepest regret that our Prime Minister could not deliver Brexit. However, it is now in the best interests of the country for a new Prime Minister to come forward to lead and unify our great country."
Shropshire’s most senior Labour politician has said a general election must follow Theresa May’s resignation.
Councillor Shaun Davies, the Labour leader of Telford & Wrekin Council, said it would not be acceptable for the next prime minister to be chosen by the Tory party membership, without facing a country-wide public ballot.
Councillor Davies said he had sympathy with the Prime Minster, but that the country now needed a government which is able to govern.
He said: “I think it has been a long time coming and I think many people have predicted this for a very long time.
“It has been a government that has not been governing for a least a year, distracted by their own divisions.
“It is a sad day for the prime minister personally and when you listen to her you would have to be inhuman not to feel sorry for her.
“But I am now fearful for what the Conservative Party does, choosing a new prime minister who does not have a mandate from the country. It raises some big issues in terms of democracy and an immediate general election is needed to re-set the make-up of parliament.”
Former Shropshire Council leader Keith Barrow said the hallmark of her time in the job as "failure and pigheadedness".