But after meeting Mrs May he told this paper: "I've been to see the prime minister and received important undertakings and chose to vote to give the prime minister the authority and freedom to negotiate the best deal she can".
While in the end, only two Tory MPs - Ken Clarke and Anna Soubry - voted against the government, there were clashes over how much of a say Parliament should get as the United Kingdom leaves the European Union, with one side accusing the other of trying to "wreck" Brexit - and being accused in turn of being "zealots" who wanted to sideline Parliament.
He accused the Government of trying to "limit" Parliament's role and called for another referendum once ministers' chosen path becomes clear.
- After a rollercoaster week of Brexit rows within her government and with Brussels, British Prime Minister Theresa May will on Tuesday seek to avoid another setback in a long-awaited showdown with parliament.
The debate, which lasted for almost three hours, was split down the usual non-partisan lines that have emerged as a result of Brexit, with the likes of Labour's Kate Hoey and John Mann saying they would back the Conservative government, while Tories including Ken Clarke and Anna Soubry spoke in favour of Grieve.
Earlier this year, Lee had called on the government to release its economic impact assessments of Brexit and suggested the government change tack in talks with the European Union, underlining the deep rifts in his party over the best way to manage Britain's exit.
The Government's compromise is that a minister would come to the House within 28 days of a deal being rejected to tell MPs what will happen next, but an amendment tabled by former attorney general Dominic Grieve would insist on a binding Commons motion.
In what is likely to be a highly-charged appearance before the backbench 1922 Committee on Monday, the Prime Minister is expected to say that the way MPs vote will send a message.
Yet, the Labour camp is split on the Brexit issue between pro-Leave MPs ready to vote with the government, and rebels who've come out against their own party's amendment to support the country's membership in the European Economic Area. Sources have said the government is happy to implement the first two points and will discuss the last one.
The Government has won this key vote, but not without having to make some significant concessions.
The parts of his amendment which he expects to be taken forward by ministers provide a mechanism by which Parliament has to be consulted by the end of November in the event of no deal or if a proposed agreement is rejected, he said.
There is a gap between what the Tory Remainer rebels think the prime minister promised them and what the Brexit Secretary David Davis thinks has been promised.
Ukip leader Gerard Batten said: "The only "meaningful vote" was the verdict of the people in referendum of 23rd June 2016".
Brexit protesters outside Parliament House.
On Tuesday, parliament will also debate other amendments, including a challenge to the government's plan to put March 29, 2019, or "Brexit Day", into law and an attempt to toughen a commitment to ensure a frictionless border between Northern Ireland and the neighbouring Irish Republic, which will remain in the EU.
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