The plea came as the EU (Withdrawal) Bill returns to the Commons tomorrow with ministers seeking to overturn a raft of amendments by the House of Lords meant to keep Britain close to the EU after Brexit.
In a statement on his website, Lee, a former GP, said it seemed inevitable that the "people, economy and culture of my constituency will be affected negatively" by leaving the European Union, and he called on the government to give the country another referendum on the final Brexit deal.
In the months that followed, May struggled to assert her authority over her party and government, with a string of ministers resigning from the Cabinet and disunity over Brexit among those who remained around her top table.
His resignation came hours before British Prime Minister Theresa May faces crunch votes in parliament and a potential showdown with pro-EU rebels in her ruling party over whether parliament can prevent a no-deal Brexit.
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He also noted that his youngest daughter suffers from a congenital heart defect, and filed letters his behalf from US Sen. He said that a state-provided attorney had talked with Villavicencio, who is being held at a New Jersey facility.
"But if the Lords amendments are allowed to stand, that negotiating position will be undermined".
'But the message we send to the country through our votes this week is important.
"This isn't about narrow party politics", she told BBC Radio 4's Today programme.
Lee, who was Parliamentary Under-Secretary of State at the Ministry of Justice, has quit the front bench so he can vote against the government on the "meaningful vote" amendment.
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These conditions extend to apps providing cryptocurrency futures trading, and other crypto-securities or quasi-securities trading. Apps may not mine for cryptocurrencies unless the processing is performed off device (e.g. cloud-based mining).
The government has also tried to stem rebellions by offering its own options - on the "meaningful vote", it has proposed a 28-day breathing space if parliament rejects a Brexit deal.
The Government is against the plan, believing it sends the wrong message to Brussels regarding the UK's negotiating goals.
Other amendments from the Lords to be debated Tuesday include transferring the EU's Charter of Fundamental Rights into United Kingdom law and one forcing the government to negotiate to remain in the European Economic Area (EEA) like Norway.
The speech will come on the eve of two days of debates and voting on amendments to the EU Withdrawal Bill, which is scheduled to last 12 hours.
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Traffic was held up in the steamy midday sun and scores of bystanders were penned in by police when Trump went to meet Lee. At the top of the expanded meeting, Trump said he and Kim "will solve" the problems presented by a nuclear North Korea .
Mrs May can count on the support of the 10 Democratic Unionist Party (DUP) MPs - secured as part of the confidence and supply deal - but not some Tory backbenchers who voted to remain.