Michael Portillo claimed the Prime Minister should have been ready to be “shouted at”, but instead wanted an “entirely controlled situation”.
He compared her to Jeremy Corbyn who spoke with victims at a refuge centre in the area and was pictured embracing a woman searching for a missing 12-year-old girl.
More broadly Mr Portillo, who held two other cabinet posts, said he believed Ms May is a “proven loser”, that her days were numbered and that he would be “amazed” if she was in charge at the end of the summer.
Defence minister Tobias Ellwood said the Prime Minister was unable to meet residents due to security concerns, while Sajid Javid defended his leader, arguing that people show their emotions in different ways.
The furore over Ms May's visit to the scorched Grenfell Tower, follows a botched election campaign which exposed her discomfort at being in the public eye and saw her criticised for relying on repetitive slogans.
Appearing on the BBC's This Week, Mr Portillo said: “Alas, Mrs May was what she’s been for the last five or six weeks, and that is to say she wanted an entirely controlled situation in which she didn’t use her humanity.
“She met in private with the emergency services, a good thing to do no doubt. But she should have been there with the residents, which is what Jeremy Corbyn was. And he was there hugging people and being natural with them.”
He went on: “The Prime Minister would have been shouted at by the residents, but she should have been willing to take that. You have to be prepared to receive people’s emotions and not be so frightened about people.”
Mr Portillo, who served in John Major’s cabinet in the mid-90s, lamented that the Conservatives were in a “terrible quandary” over how they should move forward.
He said: “She’s not going to be Prime Minister for very much longer. I’d be amazed if she made it to the conference, which is in October.
“The only person who could lead the party who is a proven winner is Ruth Davidson. Theresa May is a proven loser.”
On Question Time last night, Tory minister Tobias Ellwood blamed “security concerns” for the decision to keep the Prime Minister away from local residents.
On Sky News, Communities Secretary Mr Javid said Ms May had wanted to make sure emergency services had all the resources they needed and had released extra funds to ensure they did.
Speaking yesterday, Ms May said: “Right now, people want answers, and it’s absolutely right and that’s why I am today ordering a full public inquiry into this disaster.
“We need to know what happened, we need to have an explanation of this, we owe that to the families, to the people who have lost loved ones, friends and the homes in which they lived.”
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies