The bill "is potentially a harmful act for this country, it would damage our reputation and I think it will make it harder to strike trade deals going forward", he told Channel 4 News.
While the prime minister had a comfortable majority in Monday night's vote, with only two Tories voting against him for now and others abstaining, there will be opportunities for further rebellions as the bill passes through the Commons.
"Their hardball approach must be met in equal measure if we are to emerge from Brexit with a fair arrangement.I therefore remain focused on supporting the government's negotiation stance to secure a free trade deal with our European partners, protect our economic interests, and thereby ensure that the safety net provisions in this Bill never need be deployed".
"I don't take on board this kind of piety that people have suddenly found about, 'oh we don't disobey worldwide law or whatever, '" she said.
Meanwhile, British ministers say the bill, which explicitly states that it could be inconsistent with a host of worldwide laws, is meant to clarify ambiguities - particularly over Northern Ireland - and act as a safeguard in case trade talks fall.
"Violating the terms of the Withdrawal Agreement would break worldwide law, undermine trust and put at risk the ongoing future relationship negotiations", the European Union said in a statement after an in-person emergency meeting with UK's Cabinet Minister, Michael Gove in London last week, adding that it is up to the United Kingdom to rebuild this trust. Starmer also said he suspects Johnson's latest move may be created to gain leverage in the talks.
Martin was speaking on RTÉ's The Week in Politics after Boris Johnson's Conservative Government introduced the Internal Market Bill in British Parliament. He insisted the EU had made unfair demands to "exert leverage" in Brexit trade talks, including threats to block food exports, and said the Internal Markets bill would prevent European negotiators from taking an "extreme and unreasonable" stance on the withdrawal agreement.
Sir Bob Neill, the Conservative MP behind the rebel amendment, said the Prime Minister's promise of a vote did not provide "enough scrutiny for such a constitutionally significant issue".
Conservative MP Rehman Chishti resigned as Boris Johnson's special envoy for freedom of religion or belief, citing his inability to support the Internal Market Bill.
Neill's cause was boosted by the intervention of former Attorney General Geoffrey Cox, an influential Conservative backbencher, who wrote in the Times that Johnson's approach does "unconscionable" damage to Britain's global reputation. He posted: "As an MP for 10 years and former barrister, values of respecting rule of law and honouring one's word are dear to me".
The pound fell 3% last week on fears of a no-deal Brexit.
"Either he wasn't straight with the country about the deal in the first place or he didn't understand it", Miliband said.
"What's interesting for me is not just the opposition that you're seeing from former Prime Ministers like Tony Blair or David Cameron or John Major it's hard-line Brexiteers, people like Lord Lamont, people like Lord Howard, saying this isn't Brexit", Mr Varadkar added. "It's his mess. It's his failure".