Comedian Rowan Atkinson, best known for his roles in Blackadder, Mr. Bean and Johnny English, has defended Johnson.
"You should really only apologise for a bad joke".
"I think a lot of your listeners will be deeply anxious about the state of our democracy and free speech", he told talkRadio.
"But I think what's important is that the procedures of the party now take place".
Mr Johnson is facing investigation by an independent panel following complaints that his comments on the burka breached the Conservative Party's code of conduct.
It's not the first time Atkinson has got involved in controversy around free speech.
Condemnation of the comments also came from the Chairman of the Jewish Leadership Council Jonathan Goldstein, who took to Twitter, posting: "Boris Johnson's comments totally disgraceful".
The Conservative code of conduct says members should "lead by example to encourage and foster respect and tolerance".
Labour, which has faced continued pressure over its handling of anti-Semitism in the party, fell three points to 35%.
Johnson's comments were criticised by Muslim groups and politicians including Prime Minister Theresa May, who urged Johnson to apologise.
But the former Cabinet minister, who is on holiday overseas, has made no response.
Under party rules, the head of the investigation may dismiss complaints that are obviously trivial or lacking in merit and those which can not fairly be investigated.
Commenting on Lord Sheikh's remarks, Mr Mitchell said: "I am horrified to hear about the communications that Lord Sheikh has had".
Of the 75 emails he had received about the issue, 15 were supportive while the rest "were vile".
"And I don't believe that just because somebody takes offence that means that therefore there has to be an inquiry which means that the individual can be shut down in terms of their ability to say what they believe".