The actor, best known for playing Mr Bean and Blackadder, described the remarks as amusing.
But Mrs May, amid calls from Tory peer Lord Sheikh for Mr Johnson to be removed from the party, has insisted Mr Johnson apologise, saying his remarks "clearly caused offence".
"You should really only apologize for a bad joke. On that basis, no apology is required".
The internal Tory process looking at Mr Johnson's comparison of Muslim women in face coverings with "bank robbers" or "letter boxes" was automatically triggered on Thursday after party headquarters received several complaints.
A panel including one independent figure, one representative of the voluntary party and one nominated by the backbench 1922 Committee, will look into complaints that his comments breached the Conservative Party's code of conduct.
He explained there was a complaints procedure within the Conservative Party and that the Party had a mechanism for dealing with these issues.
"I think it's a very dark day for our democracy and free speech and I'm deeply anxious that this policy is being adopted by the Conservative Party, if we're not the party of free speech, then who is?"
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".
Mr Johnson was reacting to news the first person had been fined for wearing a full-face veil in public in Denmark, and used his Daily Telegraph article to warn against a similar "heavy-handed" movement in the UK.
He called it an "almost flawless visual simile" and added that is was a joke that, whether Mr Johnson apologises for it or not, "will stay in the public consciousness for some time to come".
Slightly more (48%) thought he should not apologise for the comment, than those who thought he should (45%).
A hundred Muslim women who wear the niqab or burka have signed a letter to Lewis, calling on him to withdraw the Conservative whip from Johnson and launch an independent inquiry into Islamophobia in the party.
Protesters took part in a demonstration outside his constituency office on Thursday afternoon.