The pound strengthened 0.3 percent against the dollar to $1.3424 after parliament voted to back the government on several amendments to the European Union withdrawal bill.
Today the government avoided an embarrassing defeat on a key Brexit vote by offering concessions to Remainer Tory MPs.
Lee's resignation came as May's fragile minority government scrambled to shore up support among lawmakers before two days of debate and votes in the House of Commons on its flagship Brexit bill. Mr Grieve's proposal will now be added to the legislation.
But Solicitor General Robert Buckland publicly implied that Government would be accepting part of Grieve's amendment, and said that a "structured discussion" would take place with rebels.
The government won the vote after last-minute horse-trading, some of it in the open on the floor of the House of Commons - some behind closed doors. "It was the prime minister who I sat in front of this afternoon and who gave us those assurances".
However, despite backing down, pro-Remain Tories signalled they would not be easily consoled by a compromise offered by ministers.
The government was putting a combative spin on the concessions Tuesday evening: "The Brexit Secretary has set out three tests that any new amendment has to meet - not undermining the negotiations, not changing the constitutional role of Parliament and Government in negotiating global treaties, and respecting the referendum result", a spokesperson for the Brexit department said in a statement.
"The government have conceded that this is necessary and I expect to see a new amendment to cover this situation soon".
Conservative lawmaker Phillip Lee, who had voted to remain in the European Union, resigned as the justice minister so he could speak out against the policy on Brexit.More news: What Really Sparked Trump's Outrage Over Trudeau's Statement?
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The Lords passed an amendment stating that Brexit can not go ahead until a minister has presented a report setting out what the United Kingdom has done to try to negotiate continued customs union membership.
MPs voted down the Lords amendment on "sifting regulations" by a majority of 22.
May urged Conservative lawmakers to back the government and show "that we are united as a party in our determination to deliver on the decision made by the British people".
Davis warned lawmakers the government would never allow them to "reverse Brexit" and called on them to back its own amendment, which proposes a 28-day breathing space if parliament rejects a Brexit deal, during which the government would have to make a statement on its plans. The government fears a weakened negotiating position.
Grieve's proposal also suggested if no deal was reached by February 15, the government would be required to allow the House of Commons to set the terms of the deal.
Pro-EU lawmakers, however, welcomed it as a signal that the government was moving towards ruling out a hardline "no deal" Brexit.
She was so supportive towards the former attorney general, as he argued for Parliament to have a "meaningful vote" on the terms of the Brexit deal, that it seemed probable she would join the Euro-rebels in voting for it....
"However, facing the prospect of a humiliating defeat Theresa May has been forced to enter negotiations with her backbenchers and offer a so-called concession".