Mrs May's closest aide quit and the Education Secretary was forced to make a humiliating apology as David Cameron asserted his authority to restore "team discipline" at the heart of his Government following the row over the way Islamist extremism is handled.
But Mrs May faced further questions about her personal involvement in the release of a letter from her to Mr Gove raising concerns about the Department for Education's response to the allegations of a plot by Muslim hard-liners to take over the running of Birmingham schools.
The Home Secretary's special adviser Fiona Cunningham resigned following the investigation ordered by the Prime Minister into the bitter row.
Mr Gove wrote to apologise to the Prime Minister and senior Home Office official Charles Farr "in acknowledgement of his role" in the row.
But shadow home secretary Yvette Cooper said Mrs May should also explain her actions, including whether she breached the ministerial code which sets out the standards of conduct for members of the Government.
She told BBC1's Andrew Marr Show yesterday: "We've seen the Education Secretary apologise, the special adviser to the Home Secretary resign, but we've so far heard nothing from the Home Secretary even though it looks pretty clear that she has breached the ministerial code by writing and then authorising the publication of this letter.
"Well the Prime Minister's responsible for enforcing the ministerial code. He needs to act and to make sure that that happens, at the same time as making sure they also address these more important issues about what's happening in schools and communities."
The letter from the Home Secretary to the Education Secretary questioned his department's response to the Islamist "Trojan horse" allegations in Birmingham schools and was released in retaliation for comments attributed in The Times to an unnamed source - but apparently Mr Gove himself - criticising counter-terrorism chief Charles Farr's approach to preventing the spread of extremism.
Ms Cooper said: "I think Theresa May needs to come out publicly and answer what she did to publish this letter. The ministerial code says that ministerial correspondence and cabinet committees shouldn't be published, it should be private."
lMs May is being called on to explain her behaviour by the Commons Home Affairs Select Committee, its chairman Keith Vaz has said.