The Government should look at either a customs union or European Economic Area (EEA) membership as a fallback to avoid leaving the European Union without a withdrawal agreement, the Exiting the EU Committee suggested.
The recommendations came in a report released on Tuesday that three arch-Brexiteers who sit on the committee - Jacob Rees-Mogg, Andrea Jenkyns and Sammy Wilson - refused to endorse.
It said that a no-deal scenario “would leave many businesses facing huge uncertainty”.
Committee chairman Hilary Benn said that with time running out to secure a withdrawal agreement there were “significant problems yet to be resolved”, with the Irish border backstop the main sticking point.
He added: “We’re urging the Government to concentrate on getting a deal to ensure the continuation of tariff and friction free trade which is so important to the future of our economy.
“If the Chequers Plan is not acceptable as a basis for that, then the Government will need to find a different approach urgently.
“Alternatives are either an EU-UK Customs Union and alignment on relevant EU rules, or EEA membership and a customs union, but neither are Government policy.”
Number 10 has consistently ruled out similar plans. Earlier in September former skills minister Nick Bole suggested the UK should take up temporary membership of the EEA and the European Free Trade Association (EFTA) following EU withdrawal in 2019 to allow time for a free trade agreement to be negotiated.
But Theresa May’s official spokesman said that this proposal would not deliver on the wishes of British voters expressed in the 2016 referendum.
Courting either option would also put Downing Street on a seismic collision course with hardcore Brexiteers who feel that Chequers already leaves the UK too close to the EU.
Tory hardliners Mr Rees-Mogg and Ms Jenkyns joined DUP MP Mr Wilson in refusing to endorse the report, entitled The progress of the UK’s negotiations on EU withdrawal from June - September 2018.
Those who supported the report included Brexiteer former culture secretary John Whittingdale.
The report notes that a no-deal Brexit would have “significant consequences for the UK and the European Union”, adding: “We remain of the view that this would be chaotic and damaging for the UK economy and would leave many businesses facing huge uncertainty.
“In many areas, the Government’s no-deal contingency planning rests on the European Union taking reciprocal action to minimise harm.
“This assumes that, if no deal is reached, there would be sufficient goodwill between the two sides that specific sectoral agreements could still be reached to minimise damage to the UK and EU economies.
“When we met Michel Barnier, he ruled this out and we would ask the Government to respond to his statement.
“Furthermore, even if both sides wanted to work together to find ways to mitigate the worst effects, it is far from clear that there would be enough time to negotiate, agree and implement any sectoral deals before the UK leaves the European Union at the end of March 2019.”