Less than 6% of MPs and peers have asked to see the Brexit impact papers, which were released under tight security after a House of Commons battle with Brexit secretary David Davis.
The Department for Exiting the European Union revealed that 83 parliamentarians have visited the restricted access reading room where they were placed last December.
It made the disclosure after a freedom of information request by Citizens4Britain, the group behind the Tories Against Brexit campaign group.
Simon Allison, the former Tory party candidate and entrepreneur who made the FoI request, said that from 1,450 MPs and peers, it amounts to less than 6%.
DExEu wrote to him on 22 June and said in total “there have been 89 visits by 83 parliamentarians” to the room where the economic impact statements are kept.
The disclosure comes just days after it was revealed that Davis has spent just four hours in meetings with the European commission Brexit negotiator Michel Barnier.
As the cabinet prepares for a showdown meeting at Chequers to decide whether to soften red lines on the customs union and the single market, Allison called for a “poll tax moment”, a reference to Margaret Thatcher decision to shelve her flagship policy after rioting in Trafalgar Square against a universal household charge in 1990.
“We need MPs ... to go to Theresa May and say, ‘This is not working, there is no planning for no deal, so the no-deal option doesn’t exist,’” said Allison.
When confronted with the possibility of breaking a manifesto pledge, he said: “The Tories are a pragmatic party and can say, ‘We got it wrong, and we are willing to be brave and say that and we are going back on our manifesto promise.’”
A Tory minister, Richard Harrington broke ranks with May on Wednesday to declare that crashing out of the EU without a Brexit deal would be “completely disastrous” for business.
Harrington said Tory colleagues who criticised companies for raising concerns about the impact of Brexit “don’t really know how business works”.
“There is a increasingly big block of Tories, some remainers, some soft Brexiters who are frustrated that the hard Brexiters have had control of the arguments,” said Allison. “But these 60-80 MPs are arguing from an ideological point of view and allowing ideology to trump the facts.
“MPs are allowing them to turn the party into a party that is anti-business, anti-EU and anti-union, that’s not our party of the last 40 years.
Although the Brexit impact papers were subsequently dismissed by critics of the government as superficial, Allison says the lack of visits to the reading room betrays a lack of interest in the facts around Brexit.
Citizens4Britain is a Conservative supporting group, which includes Nicolas Maclean, a former adviser to Margaret Thatcher, and Neil Carmichael, a former Tory MP for Stroud.
