Conservative MP Andrew Bridgen is the first Tory reported to have submitted a letter declaring no confidence in Theresa May.
The letter was revealed by Ross Kempsell - who will join talkRADIO as Political Editor this summer - on Twitter.
If 48 MPs declare they have no confidence in the Prime Minister, it will trigger a leadership contest.
They must submit their letters to the 1922 Committee chairman Sir Graham Brady.
The 1922 Committee is made up of Conservative backbench MPs.
Jacob Rees-Mogg 'supports Prime Minister'
Jacob Rees-Mogg told talkRADIO earlier today (July 10) that he did not know if any MPs had submitted a vote of no confidence.
“I have no idea, Sir Graham Brady has made it very clear that he will not give anybody any indication of how many letters he has received,” he said.
“In a vote of confidence in the House of Commons I would support the Prime Minister that’s because I don’t want to have another General Election, there isn’t a vote of confidence in either case at the moment, I don’t think many people want another election, we only had one a year ago.”
Nigel Farage 'would consider return to politics'
Nigel Farage said he was pleased former Brexit Secretary David Davis and former Foreign Secretary Boris Johnson had resigned.
Speaking to James Whale on talkRADIO, he said: “Frankly, what came out of Chequers was a complete betrayal not just in the way people voted in the referendum but how they voted in the general election.
“Mrs May was very clear in her manifesto what was going to happen; that we were leaving the single market, we were leaving the customs union and we’d be an independent country - and what came out of Chequers is unacceptable.
“I’m pleased David Davis has resigned, I’m pleased that Boris has decided to step aside and I think this Prime Minister needs to go.”
He added that he’d consider returning to Ukip to fight the Prime Minister’s plans.
“We will not get a clean, democratic Brexit under Theresa May and if the Conservative Party don’t come to their senses, then yes, when there is a leadership contest in Ukip at the end of March next year, then I would seriously consider throwing my hat back in the ring.”
The negotiations with the European Union appear to have deteriorated into a state of complete capitulation. We have to deliver Brexit or we will be punished at the polls at the next general election.
All we have asked from the Prime Minister, is that she sticks to what she has promised on repeated occasions, when she declared that 'Brexit means Brexit' and pledged to take back control of our money, borders and laws. But it now appears that those promises are all a pretence and a charade intended to dupe the electorate, which is an insult to their intelligence.
Therefore, in the interests of our country and the future of the Conservative Party, I feel the time has come for a new leader and so I am writing this letter to inform you that I have no confidence in the Prime Minister.