The former skills minister was the campaign manager for Michael Gove’s unsuccessful bid for the leadership following David Cameron’s resignation.
As the show’s presenter Jo Coburn pushed the politician to talk about the backstabbing that consumed the Tory party in the wake of the Brexit vote, Mr Boles appeared unimpressed.
Attempting to skate over the subject, he said: “There were a lot of people who tried to persuade him to stand. He did have deep reluctance so ultimately things followed a different course, and of course it would have been much better if we’d been successful but it’s all water under the bridge now and we’ve all got on with it and we have a great new prime minister and a great new foreign secretary and Michael and I are supporting them.”
Laughing off Mr Boles’ response, the BBC journalist said: “I’m not going to let you off the hook that easily. It’s not that much water under the bridge, it wasn’t that long ago. What were the thought processes going through yours and Michael Gove’s mind? What made him do it?”
A frustrated Mr Boles retorted: “I’m sorry Jo, I’m not going to go into all of the details, it’s not the basis on which you asked me to come onto this show and I’m not willing to discuss it.
“It was a mistake obviously for Michael not to run in the first place and he accepts that and I will always regret it.
“As I say the decisions were made for the reasons they were made. Ultimately it didn’t work out and we’re now all getting on with the situation we have which actually is profoundly good for the country.
Mr Gove was accused of trying to rig the Conservative party leadership election, after Mr Boles begged MPs to vote tactically to stop the “seriously frightening” risk of Andrea Leadsom becoming prime minister.
The presenter asked if he regretted sending the “infamous message” to which he asserted: “You asked me onto this show to talk about Brexit and the way in which Brexit was going to be negotiated.
“I’m very happy to discuss that. I’m not happy to dissenter the leadership election which has long passed and which has had a very, very successful outcome.”
As the host pressed further, he threatened to leave the show, adding firmly: “Jo, if you want me to stay on the programme… we are going to have to move on”