Ken Clarke, who served in Conservative governments under prime ministers from Margaret Thatcher to Cameron, gave the unguarded comments in a Sky News studio.
He was apparently unaware the cameras were rolling as he began to chat about the contenders with fellow Conservative lawmaker Malcolm Rifkind.
His comments came as voting began in the first round of the contest to replace Cameron, who resigned in the wake of the referendum.
Whoever wins the contest will become the leader of the ruling Conservative party and, hence, prime minister.
Both men laughed as they discussed the frontrunner, interior minister Theresa May.
“Theresa’s a bloody difficult woman but you and I worked with Margaret Thatcher,” a rumpled and pink-faced Clarke said.
“I get on all right with her and she is good. She’s too narrow on her department… She doesn’t know much about foreign affairs,” he added.
He suggested May’s foremost rival Andrea Leadsom, a junior energy minister who rose to prominence campaigning to leave the EU, had been making unwise promises.
“So long as she understands that she’s not to deliver on some of the extremely stupid things she’s been saying,” Clarke said.
On Michael Gove, the justice secretary who campaigned in favour of Britain leaving the EU, Clarke recalled “wild” comments he had made about British policy in the Middle East.
“I think with Michael as prime minister we would go to war with at least three countries at once,” Clarke said.
He did not spare Boris Johnson, the former London mayor who backtracked on hopes to run for the leadership when Gove pulled his support for him last week.
“He did us all a favour by getting rid of Boris. The idea of Boris as prime minister is ridiculous,” Clarke said.
Britain’s referendum vote last month to leave the EU has unleashed political turmoil in the ruling Conservative and opposition Labour parties and triggered a string of top-level resignations.
In Tuesday’s first round of voting to chose Cameron’s replacement, who will have the task of negotiating Britain’s EU exit, May finished first with Leadsom second, though trailing well behind.
The candidates are set to be narrowed down to two on Thursday.
