The amendment to the trade bill was the latest skirmish in the bitter Brexit wars that are being fought across the Conservative benches.
Prime Minister Theresa May has bowed to pressure from Brexit supporters in her Conservative Party, accepting their changes to a customs bill that underpins Britain's departure from the European Union, write Elizabeth Piper and William James.
May narrowly avoided a defeat in parliament at the hands of the pro-EU lawmakers from her own party in Tuesday's vote, helped by four opposition Labour lawmakers who went against their party to support the government.
When asked if the amendments to the Customs Bill would increase the prospects of a no deal Brexit, Mr Wilson said: "It all depends on the reaction of the EU".
The four Labour MPs who stepped in to save Theresa May's government are Frank Field, Kate Hoey, John Mann and Graham Stringer, to whom one should add the independent Kelvin Hopkins.
Britain's European Union membership was critical to United States interests, with the policy underpinning the agenda of all UK governments since Britain entered the European Union in 1975.
A relieved International Trade Secretary Liam Fox described the trade plan as "the confident first step that the United Kingdom takes towards establishing itself as an independent trading nation for the first time in over 40 years".
"It will be the confident first step that the United Kingdom takes in establishing itself as an independent trading nation", he added.
MPs backed an amendment by 305 votes to 301 that would keep the United Kingdom in the European medicines regulatory network.
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This week's votes "showed that the hard Brexit Conservatives have the numbers to sway the government's Brexit strategy, in contrast to the Rebel Remainers who have lost or withdrawan some of their key amendments".
The commission said it found significant evidence that Vote Leave spent more than it declared by funneling cash to a small, unregistered pro-Brexit youth group, BeLeave.
The East Antrim MP also said the legal assurance that there will be no post-Brexit customs border between NI and GB would effectively kill off the so called "backstop option", whereby Northern Ireland would remain in the customs union in the event of a "no deal" Brexit.
On Monday, May infuriated lawmakers who want to keep the closest possible ties in the European Union when she made a decision to accept a number of demands by hardline pro-Brexit members.
The MP for Broxtowe told BBC Radio 4's Today programme she would be the first in the queue to give a vote of full confidence in the prime minister.
But former transport minister Mr Hammond, who joined five other Tory backbenchers in tabling the amendment, insisted its provisions were "entirely in line" with Mrs May's Brexit White Paper.
The Prime Minister is due to fly into Northern Ireland on a two-day trip tomorrow that will include a high-profile visit to the border.
Describing the government's approach as "a total and complete mess", Tony Blair said in an interview that the only way out is to hold another referendum on the issue.
"Once this thing has been started by a referendum, it can frankly only be finished by a fresh vote", Blair said.