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Demonstrators called for a vote on the final outcome of the government's Brexit negotiations during the March for the Many protest in Liverpool on 23 September
A Conservative MP says she sees no alternative other than backing another referendum on leaving the EU.
Heidi Allen becomes the latest Tory to support a new vote, saying the "right-wing" of her party had made Theresa May's Chequers Brexit plan"dead".
"They have behaved unacceptably through this and have completely tied her hands," she told the BBC.
The prime minister has ruled out a referendum on the outcome of the Brexit negotiations.
But Ms Allenwho campaigned to Remain in the EU in 2016told Radio 4's Today programme that while she would still support in principle an "11th hour" deal from Mrs May and the EU, "too many" of her partyespecially those on the rightwould not.
The South Cambridgeshire MP said she had been left with "no alternative other than askingshould we come to that, no deal, that looks like that's what's going to happenthen we need to go back to the public to decide what they want us to do next."
On what a further referendum could look like, Ms Allen suggested that it should include the option of staying in the EU under existing terms.
The People's Vote campaign group wants to give the public the final say over whether the UK leaves the EU, arguing that voters should be given a choice between leaving with or without a deal or staying on current terms.
Anna Soubry, Justine Greening and Sarah Wollaston are among the Conservative MPs who have supported a further referendum.
Ms Allen's comments come after ex-PM Sir John Major also made the case for another Brexit vote and highlighted the "completely unacceptable" attacks by certain Tory MPs on Mrs May.
Meanwhile, former foreign secretary Boris Johnson set out his "better Brexit plan" and refused to rule out a leadership challenge.
Last week Labour members voted to keep the option of another referendum on the table if parliament is deadlocked over the final outcome the government's Brexit negotiations.
The UK is due to leave the EU on 29 March 2019, and negotiations on the terms of exit and future co-operation are continuing.
The Conservative party is gathering in Birmingham for its annual conference.