"Our backstop can not be extended to the whole United Kingdom why because it has been designed for the specific situation of Northern Ireland", he said, adding that what was "feasible" for the relatively small territory of Northern Ireland was not necessarily feasible for all of the United Kingdom.
The campaign, Best For Britain, is urging British lawmakers to force a referendum on the deal - which is still to be secured by Prime Minister Theresa May with the European Union officials - before the country formally leaves the bloc.
The future of the border between European Union member Ireland and Northern Ireland after Brexit is one of the most hotly contested issues in the negotiations, with many on both sides of the border wanting to keep the current free-flowing frontier open.
"I am very concerned that by the time we have negotiated this with the European Union we will have a never-ending vassal state status", said Conservative Brexiteer Nigel Mills.
The option emerged after the EU's chief Brexit negotiator Michel Barnier rejected key elements of May's backstop plan for the Irish border. It would have signed us up to the rules of the EU Customs Union (a central pillar of Brussels rule) if it was ever activated.
It adds: "The UK expects the future arrangement to be in place by the end of December 2021 at the latest".
Belmont Stakes: Justify completes Triple Crown with wire-to-wire win
Justify was the Belmont's wire-to-wire leader, jumping to a lead out of the gate and never relinquishing it. Justify won the 150th running on the Belmont Stakes on Saturday, becoming the 13th Triple Crown victor .
"The UK is clear that the future customs arrangement needs to deliver on the commitments made in relation to Northern Ireland".
Even if he hadn't, the government's proposed backstop would have set us on the road to Remain by another name. "We are no closer to knowing the relationship Britain is going to have (with the EU)", said Jane Foley, a currencies strategist at Rabobank.
But it is likely the main focus of the meeting of the world's seven wealthiest industrial nations will be dominated by discussions around the United States president's controversial trade strategy. "I would like the British government to respect its own red lines as well", Barnier said.
Brexit secretary David Davis said Britain had been instrumental in developing Galileo's technology, and that shutting it out at this stage would delay the project by up to three years and increase the bill by an extra 1 billion euros (£0.9 billion).
Companies face an extra 20 billion pounds ($27 billion) a year in costs to comply with the customs arrangement if there is a no-deal Brexit, Britain's most senior tax official said on Tuesday.
Pro-Brexit campaign group Leave.EU have attacked Lord Malloch-Brown as a "puppet for George Soros" and chief "Remoaner", while another group, Leave Means Leave, has launched a fundraising drive among supporters to "secure the swift, clean Brexit you all voted for".