British ministers state the costs is a "safety net" in case there is no trade offer reached with the bloc, however leading European Union authorities state it weakens both the withdrawal treaty and rely on future talks.
The U.K. formally left the bloc on January 31, but existing trade rules remain in effect until the end of this year under a transition created to provide time to negotiate a long-term trade agreement.
The Reuters reported that this bill must pass through the UK's House of Commons and then the House of Lords, the upper chamber, to become a law.
Boris Johnson looks set to withdraw from significant European human rights laws in a move which could make it easier to deport migrants and more hard to sue British soldiers.
However, Cameron did not go that far, saying a proposed bill that lawmakers will vote on later today - and which the government has said would breach global law - had to be seen in the context of tough trade talks with the EU.
"I feel strongly about keeping the commitments we make; if we give our word, then we must honor it. Voting for this Bill as it now stands would be contrary to the values, I hold dearest".
"The breaking of the law ultimately leads to very long-term and permanent damage to this country's reputation", he said.
Backed by the EU, Ireland stresses the provisions for Northern Ireland were agreed by both sides to ensure fair competition after Brexit, and to comply with a 1998 peace pact that ended three decades of unrest in the province.
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Tony Blair and Sir John Major today joined forces to accuse Boris Johnson of "shaming" Britain and "embarrassing our nation" over his plans to tear up parts of the Brexit divorce deal. On Monday a third, David Cameron, said he had "misgivings".
Meanwhile, Tory MP Rehman Chishti resigned as the Prime Minister's special envoy on Freedom of Religion or Belief (FoRB) in opposition to the clauses in the Bill.
He tweeted that as a former lawyer, "values of respecting rule of law and honouring one's word are dear to me".
Mr Johnson's potential opt-outs could tee up a fresh clash with Brussels after tensions grew in recent days when the PM unveiled plans to tear up parts of his original Brexit divorce deal. That declaration of victory was key to Johnson's successful December 2019 election campaign.
"But the government collectively here also has a responsibility - we've got to resolve any conflict, that's what we will do".
"I am extremely concerned we are placing severe restrictions on people's liberties without any recourse to parliament", he told MPs.
To this end, London and Brussels initially negotiated a temporary Irish backstop in 2017-18 wherein, the whole of the United Kingdom would continue in the EU customs union until an alternative was in place.
"I do think being asked to put this country, members of this house and our constituents, on the wrong side of the law before we've exhausted all other options".
He said it's a good thing that talks are continuing as the most important thing for Irish farmers and exporters is that a free trade agreement is secured and tariffs and quotas are avoided from the start of next year.
European legislators have actually alerted they would not authorize any brand-new trade offer unless the withdrawal arrangement was totally executed, while there is likewise talk of possible legal action.