The House of Commons approved the bill by 340-256 votes late Tuesday. Next, the law goes to the upper house.
Although the bill has been criticized even within the Conservative Party, it is expected to pass through the upper house as well.
As an exceptional statement, all the surviving former prime ministers of Britain, i.e. Sir John Major, Tony Blair, Gordon Brown, David cameron and Theresa May, have expressed opposition to the bill.
The current Prime Minister, Boris Johnson, has admitted that the controversial law violates in key respects the already signed EU resignation agreement and international obligations.
Among other things, the law allows British government ministers to unilaterally rewrite the clauses included in the resignation agreement.
The EU threatens to take Britain to court unless it repeals by Wednesday those clauses that violate the divorce agreement.
Minister of the British Government Michael Gove characterizes the bill as vital to ensure smooth trade between the four British countries.
The British government is also rejecting warnings from US Special Envoy for Northern Ireland Mick Mulvaney that the Internal Market Act will jeopardize the Northern Ireland Peace Agreement.
With these prospects, the final round of talks between the EU and Britain began on Tuesday and will end on Thursday 1 October.