The sticking point in the EU-UK negotiations, so far, has been around the proposed customs backstop - an arrangement that will apply to the Irish border after Brexit, if a wider deal or technological solution can not keep it as frictionless as it is now.
Shadow Scotland Secretary Lesley Laird said the fact that no Scottish Conservative MPs rebelled against the government meant "Ruth Davidson's pledge that her MPs would stand up for Scotland was nothing short of a lie".
"However, I believe it is a basis on which more serious negotiations can now start".
May denied a suggestion in parliament that her Brexit plan was dead, and her spokesman said the decision to accept those amendments were "consistent" with the white paper policy document ministers agreed earlier this month.
A 10th member of her government quit on Monday in order to vote against her - this time in favour of a soft Brexit - and Mrs May needed the backing of three rebels from the opposition Labour Party to win.
"People are using terms like "cliff edge" and "no deal" with negative connotations, but we trade on World Trade Organisation Terms with 80 per cent of the world, including the single largest country we trade with, America".
She also saw off an attempt by pro-European Union rebels in her own party require the government to try to negotiate a customs union arrangement with the EU if, by January 21, 2019, it had failed to negotiate a frictionless free trade deal with the bloc.
12 noon Prime Minister's Questions - These sessions are getting longer and longer.
During his visit Mr Jones will give a speech in which he is expected to reflect on Theresa May's White Paper and discuss how both sides can work together to secure a Brexit deal before the United Kingdom leaves the European Union in March 2019.
Trump calls the European Union, Russia, and China 'foes' of the US
The United States has no extradition treaty with Moscow and can not compel Russian Federation to hand over citizens. The demonstrations were peaceful and crossed political party lines to protest against both Trump and Putin.
Tour de France stage 6 -- Dan Martin sprints to win
Another hilly stage awaits the cyclists on Thursday, this time a 181-kilometer stretch from Brest to Mur-de-Bretagne Guerledan. Sagan, who won his third consecutive road race championship previous year , rode to victory in Sunday's flatter second stage.
Envoy hopes Trump, Putin have in-depth dialogue
Of the summit as a whole, he said: "I'm not going with high expectations" but insisted: "I think it's a good thing to meet". Maas welcomed the meeting, at which the U.S. president has said he will raise the issue of nuclear weapons reduction.
Taoiseach Leo Varadkar has sought to calm nerves over a potential hard Brexit, saying amendments to the British government's customs bill would not alter Dublin's position.
Eurosceptic MPs had targeted her government's customs legislation to try to toughen up her plans to leave the European Union, but instead of facing them down and fuelling tensions, her spokesman said the government would accept their four amendments.
British voters chose to leave the European Union in a June 2016 referendum.
The Electoral Commission said the "Vote Leave" group, backed by senior politicians including former foreign secretary Boris Johnson, failed to declare 675,000 pounds ($894,000) it spent with Canadian data firm Aggregate IQ.
"On the other hand, if they remain as intransigent as they have been, then there is a likelihood we will finish up with no deal".
Mrs May was invited to visit the border by DUP leader Arlene Foster when she held talks with the Prime Minister at No.10 a fortnight ago.
The MP for Broxtowe told BBC Radio 4's Today programme she would be the first in the queue to give a vote of full confidence in the prime minister.
The government has only narrowly avoided defeats on key Brexit legislation in recent days, which has further undermined confidence in the government's ability to pass the required legislation to ensure a smooth and orderly Brexit.