Another Conservative MP has signalled she could quit her party to join MPs in the new Independent Group being set up in parliament.
While she said she is not ready to leave now, she said she was “not going to make any decisions” before waiting to see how the prime minister acted in the coming days.
It comes as Ms May is under increasing pressure to rule out a no-deal Brexit, and ahead of a backbench attempt to do just that in the coming days.
Asked about the departure of her ex-Conservative colleagues Anna Soubry, Heidi Allen and Sarah Wollaston, Ms Sandbach told BBC Radio 4’s World at One: “I read their reasons for leaving and it’s hard to disagree with them.”
Asked if she might quit, she said: “I’m not going to make any decisions, I want to see what the prime minister does and who she is listening to in the party, because it seems to me that it is irresponsible to kick this can down the road yet again.”
She said she would back the plan being brought forward by Labour MP Yvette Cooper and ex-Tory minister Oliver Letwin to delay the UK’s departure if Ms May fails to get her plans approved by the commons.
The Cooper/Letwin proposal will be voted on by colleagues on Wednesday, with Ms May and Brexiteers arguing that it will weaken her negotiating hand in Brussels.
On Sunday, Ms May confirmed that she would put off bringing a new Brexit deal for MPs to vote on until 12 March at latest, just 17 days before the UK is due to drop out of the EU on 29 March – something Ms Sandbach branded “irresponsible”.
She added: “I have businesses in my constituency who are desperate to know what the position is going to be, and to postpone it for such a long time, is to my mind, irresponsible.”
In comments that echoed grievances set out by the MPs who left her party, she went on: “I’m really frustrated at the way the PM only seems to listen to a small faction in the Conservative Party and is not willing to listen to Parliament as a whole.”
The three ex-Conservatives joined up with eight former Labour MPs to create the Independent Group, which had its first formal meeting to lay out basic structures on Monday.
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