The Prime Minister has been facing growing pressure from Brexit supporting MPs angry with the way she is handling the divorce negotiations.
The UK divorce deal unveiled in December highlighted that the UK will pay out between £35billion and £39billion to the EU as the price for leaving the bureaucratic trade bloc.
Mr Humphrys said: "Brexit is the most important issue facing this country and the Conservative party.
"Prime Ministers are meant to lead. Theresa May is not!"
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At a fundraiser, last Thursday, around a quarter of the 50 Conservative financial backers present called for Mrs May’s resignation, according to one donor at the meeting.
But Tory MP Johnny Mercer rebuked Mr Humphrys' claims, saying the Prime Minister was keeping the party "together."
He told the Today programme presenter: "They are meant to lead and she is leading because she has these two sides who are diametrically opposed on some issues and the party is being kept together.
"Brexit is the biggest issue we are facing at the moment and it will configure how we look going forward from 2019 when we leave the European Union but it is not the defining issue for the Conservative party.
Prime Ministers are meant to lead! She is not!
"The European Union is an issue that there plenty point of view on but I didn’t join the Conservative party to talk relentlessly about Europe."
During an official visit to China Mrs May struck down talks about risks to her leadership, remarking she will continue to "serve her country and party" to strike a beneficial deal with the European Union.
She said: "I've said very clearly that throughout my political career I've served my country and I've served my party. I'm not a quitter. I'm in this because there is a job to be done here and that's delivering for the British people and doing that in a way that ensures the future prosperity of our country.
"The idea that we are about to complete the negotiation with the EU about our future relationship is wrong. We are just at the very beginning of that process of negotiating with the EU. We will be out there ensuring that the deal we get delivers on what the British people want. That's what this is about."