One option being considered by the British government is a "customs partnership" that would see the United Kingdom collect tariffs on the EU's behalf at ports and airports.
"Ideas obviously are evolving as we go along and the prime minister said there are a number of ways to proceed".
Under the customs partnership plan, Britain would collect tariffs on the EU's behalf at ports and airports, passing on a share of the cash to Brussels.
Francis Maude, senior adviser at Covington and once a Tory lawmaker, said that a customs union with the EU would make it hard for Britain to negotiate trade deals elsewhere.
Sajid Javid, the new Home Secretary and Remain voter, switched sides to join Boris Johnson, Michael Gove and other Brexiteers in arguing that Mrs May's preferred option for a customs deal should be "killed off".
The ERG said technological solutions should be found to avoid a hard border in Ireland in its report rejecting the customs partnership.
On Tuesday David Davis was been called on by the Northern Ireland Affairs Committee to explain his vision of a post-Brexit border on the island of Ireland.
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The report reiterates previous warnings to May's government that any United States administration - particularly one led by President Trump - will be keen for Britain to lower its standards in areas like agriculture.
The warning, which arch-Hard Brexiteer Jacob Rees-Mogg on BBC Radio 4 denied was an ultimatum to the PM, is the latest in a string of interventions by elements of the Conservative Party, whose supporters overwhelmingly backed Brexit and who fear that Mrs May and figures such as Chancellor Philip Hammond may seek to dilute the degree of separation from Europe.
But by leaving the question open May has been vulnerable to attempts both in the upper and lower houses of parliament to try to force the customs union back onto the agenda. "So, there's a variety of mechanisms, but they don't require border infrastructure".
Conservative MPs pushing for a softer Brexit are also adamant that the United Kingdom needs to maintain customs ties with the European Union to avoid damaging business.
Brexit-supporting ministers are leaning towards her alternative suggestion of a "streamlined arrangement" using technology to minimise customs checks but not eliminate them.
"We will look at the amendments, but the fundamental point is that the bill left the House of Commons in a way that could deliver a smooth Brexit and that is how we want the bill to complete its course", the spokesman said.
Instead, he said the Government aimed to have large amounts of detail - maybe even including legal wording - "nailed down" by the formal date of Brexit. "As the Prime Minister said, there are a number of ways to proceed". They will be expected to endorse the final option once one is eventually agreed.