Bebb, who was minister for UK defense procurement, has reportedly voted against the amendment that will stop Britain from collecting tariffs for the European Union after Brexit.
According to the Daily Mirror, Bebb is understood to have resigned at the door of the lobby as he went to cast his vote.
The British government voted by 305 to 302 to support an amendment that critics said would undermine Prime Minister Theresa May's recently announced negotiating position. Bebb has reportedly been highly critical of Brexit-supporting Conservatives recently.
Last week, the British government published a white paper outlining the London vision for Brexit, which includes a free trade area for goods and separate deals for services. The United Kingdom suggested there might be new arrangements on financial services and digital commerce.
"We will leave the Single Market and Customs Union and get out of the Common Agricultural Policy and the Common Fisheries Policy. We will have that independent trade policy and a new UK-EU free trade area … We will not tolerate a hard border between Northern Ireland and Ireland or between Great Britain and Northern Ireland … None of these things are up for debate," May said on Facebook.
On June 23, 2016, the United Kingdom voted in a referendum to leave the European Union. Last March, May officially invoked Article 50 of the Lisbon Treaty, launching the process of the country's withdrawal from the bloc. The Brexit negotiations between London and the European Union started last year and are due to be completed by the end of March 2019.