Labour leader Jeremy Corbyn, responding to Theresa May's survival in the no confidence vote, said: "Tonight's vote makes no difference to the lives of our people.
"The Prime Minister has lost her majority in Parliament, her government is in chaos and she is unable to deliver a Brexit deal that works for the country and puts jobs and the economy first.
"That's why she pulled the vote on her botched Brexit deal this week and is trying to avoid bringing it back to Parliament. It's clear that she has not been able to negotiate the necessary changes in Europe.
"She must now bring her dismal deal back to the House of Commons next week so Parliament can take back control.
"Labour is ready to govern for the whole country and deliver a deal that protects living standards and workers' rights."
Liberal Democrat leader Sir Vince Cable said: "Having seen the Conservative backbenches will not support her deal the Prime Minister must change course.
"Her deal is doomed to defeat in the Commons, so she should show real leadership by putting this question back to the public in a People's Vote.
"The EU is clear that there is no more negotiating to do, so it's this deal or no Brexit. That is the choice on which every voter should now have a final say - and Liberal Democrats will campaign vigorously for the UK to remain a full member of the EU."
Scotland's First Minister Nicola Sturgeon said the result was "barely even a pyrrhic victory for the Prime Minister, who has now admitted her time in office is limited".
The SNP leader said: "She may have clung on to the Conservative leadership, but her remaining authority has been fatally undermined.
"The Prime Minister cannot - and must not - use this result to support her claim that the choice is now between her bad Brexit and a catastrophic no-deal Brexit. Parliament is simply not going to approve her deal - and is also likely to make clear that there is no majority for no-deal. Every day that she refuses to accept this is another day wasted.
"The Scottish Government and SNP will continue to make the case for Scotland's overwhelming vote to stay in Europe to be respected, and we will support any second EU referendum which has remain as an option.
"Our priority is to do all we can to stop the UK Government dragging Scotland off the Brexit cliff-edge, which is set to do so much damage to jobs, communities and living standards."
Nigel Dodds, Deputy Leader of the Democratic Unionist Party, tweeted: "The message from tonight is very clear. The Backstop must go."
