In an interview with BBC radio, Baker urged his parliamentary colleagues to kickstart a vote of no confidence in her leadership.
"I'd like Conservative members of parliament to realise we simply cannot go staggering forward any longer like this. If we can't go forwards with her deal…I'm afraid the only way to change the policy is to change the Prime Minister and I really think it' her duty to go," he said.
His comments followed May postponing a parliamentary vote on her Brexit withdrawal deal on December 10, after it became clear it would be defeated — the premier is now seeking further concessions from the European Union.
This cannot be allowed to go on https://t.co/Tkeq0amYBC— Steve Baker MP (@SteveBakerHW) December 11, 2018
Baker's not the only Conservative to call for May's exit as a result — Jacob Rees-Mogg said she must either govern or quit shortly after the postponement was announced.
"What has two years of Theresa May doing Brexit amounted to? An undeliverable deal parliament would roundly reject, if the Prime Minister has the gumption to allow it to go before the House of Commons. This is not governing, it risks putting Jeremy Corbyn into government. We cannot continue like this. The Prime Minister must either govern or quit," he said.
On November 15, Rees-Mogg announced he was submitting a letter to chair of the backbench 1922 Committee Sir Graham Brady, stating he had no confidence in May's leadership. He urged other MPs to do the same — if 48 followed suit, it could've triggered a Tory leadership challenge.
— #StandUp4Brexit (@StandUp4Brexit) December 10, 2018
However, the requisite signatures failed to materialise — and demands and threats of a no confidence vote have dogged May since her disastrous showing in the June 2017 General Election, but are yet to translate into practical action.