The government lost by 321 votes to 299 on an amendment put forward by a member of May's own Conservative Party
May has agreed an exit pact and an outline of future EU-UK ties with the other 27 states staying on together after Brexit
If she loses the vote on December 11, it will be a significant moment for Mrs. May and her country, and the margin could be crucial
May said the summit had given her the opportunity to update leaders on the Brexit deal
Gyimah said the Brexit deal could lead to "potentially crippling ourselves politically and economically for decades to come
The UK government has been keen to agree a security partnership with the EU
According to one official, speaking on condition of anonymity, May's team have now dropped this tactic in the face of protests from politicians
Opponents of the deal on either side of the argument say it fails to deliver on what people voted for in the 2016 referendum
UK's parliament will hold a total of five days of debate on the deal, beginning on December 4
The biggest question now facing the EU is whether May's divided minority government can steer the deal
A half dozen nations including the U.S. and Japan blocked a U.K. application last month, with some saying the British offer was based on a set of outdated and incomplete commitments
Brexit's move forward comes after Spanish Prime Minister Pedro Sanchez received assurances from the UK government over Gibraltar, and dropped his threat to boycott the summit
EU had released the full text of the draft political declaration on November 22
But May declined to say whether the UK would be better off outside the EU, saying only it would be 'different'
Madrid is seeking a guaranteed veto on post-Brexit relations between the EU and Gibraltar
British companies in India now employ about 800,000 people
Instead, she said Britain could build a "better future" for itself outside the European Union
The declaration establishes the parameters of an ambitious, broad, deep and flexible partnership
Its text will be considered by an EU summit on Sunday alongside a draft divorce agreement struck last week
The 65,000 to 75,000 estimate was drawn up by consultants Oliver Wyman