MPs are due to vote on the proposal later, but Brexit will dominate debate in the Commons until then following the referral of the Vote Leave campaign to the police over a breach of spending limits during the referendum campaign.
The government has tabled a motion suggesting that parliament's summer recess should begin on Thursday, five days earlier than originally planned.
Sterling dropped to a four-month low against the euro and a three-week trough versus the dollar as investors expected more Brexit challenges after Theresa May's government only narrowly won a vote on a trade bill before the British parliament.
It has been reported that more than 100 Brexiteer MPs have joined a WhatsApp group coordinating voting tactics against Mrs May, and would be meeting ahead of a vote on the customs bill.
The bill gives the government the power to set up new global trade relationships after Britain leaves the European Union next March.
Defence minister Guto Bebb voted against the Government, effectively quitting his frontbench role.
The prospect of continued drama in parliament and doubts over the future of May's "white paper" Brexit plan - which is itself only a starting point for talks with the European Union - is testing the patience of businesses that depend on cross-border trade.
Leavers led by Jacob Rees-Mogg forced the government on Monday to back four amendments to Brexit legislation, including one meant to scupper May's plans for a new customs deal. "If we don't, we risk ending up with no Brexit at all", she wrote in an article in the Mail on Sunday newspaper.
Supporters of Hammond's new clause, which was backed by MPs from the main opposition Labor Party, were given hope of success when the government lost a vote on another aspect of its EU Trade Bill by just a handful of votes, 305 against 301 for the government.
The amendments undercut parts of May's Chequers agreement, a plan for Britain's exit from the European Union that some lawmakers said watered down Britain's future independence.
Tuesday's rebellions by Tory Remainers were prompted by Mrs May bowing to the demands of Conservative Brexiteers on Monday, when the prime minister accepted their amendments to the government's separate customs bill.
But 12 Conservatives broke ranks to back the customs union measure, even though it is understood that Tory whips told would-be rebels that there would be a confidence vote that evening if it passed.
"It is with great deal of sadness that I have tendered my resignation as a Parliamentary Private Secretary at the Treasury", Mann said in a Twitter post in which he shared his resignation letter.