Lord Harris of Peckham criticised the Prime Minister’s “shell-shocked” performance at the General Election in which the Tories disastrously lost their House of Commons majority.
The peer’s intervention comes as Mrs May is continuing to face speculation about her future as Tory leader and with her party at loggerheads over Brexit.
Lord Harris told the Times: “Both sides don’t know what they want at the moment or where they want to go.
“I’d much rather have a strong Labour government than a weak Conservative one and I’m a Conservative through and through.
“I wouldn’t want Jeremy Corbyn but if you had Tony Blair when he first got in now he would be very good for this country.”
Asked if that incarnation of Mr Blair would be better than Mrs May is currently, he told the newspaper: “Probably, I think so, yes.”
On Mrs May’s rise to the premiership, the former Conservative Party deputy treasurer said he “didn’t think she had it in her”.
“I thought for the first three or four weeks she did well,” he said.
“Then she did the election and she was hopeless. She’s changed her mind too many times.
“I think she was shell-shocked but she’s got to start making decisions, or someone has… Theresa May has got a great opportunity if she lets (her ministers) work and leads them.
“I don’t know if she can lead them or not.”
Looking at potential replacements for Mrs May, Lord Harris said Boris Johnson was “a genius” but “lazy”, while Michael Gove has “no personality”.
The peer instead backed Scottish Tory leader Ruth Davidson for the top job.
“She’s very practical, very solid and won’t give in,” he said.
“She’s clever as well as growing up on a council estate. I think she’s top class.
“They should get her in as an MP… see how she gets on working her way up and I think in three or four years’ time she’d make a great prime minister.”