The group also called for a new expeditionary force to defend the Falklands from attack.
The "madcap" ideas emerged as part of an alternative Brexit plan intended to challenge Theresa May's Chequers proposals.
The blueprint – since dropped – was drawn up by Jacob Rees-Mogg's European Research Group, which includes dozens of hardline pro-Brexit Tories.
Among the suggestions was a plan to build new missile defences similar to the "Star Wars" programme first set out by Ronald Reagan.
The document said: "The UK needs a strong defence to protect these islands, which includes the insurance of a nuclear missile shield to deter aggression."
It proposed an expeditionary force to act "where there are events like the invasion of the Falklands or Kuwait that require a swift and effective military response".
The manifesto was dropped after Boris Johnson refused to endorse it, according to the Sunday Times.
Its centrepiece was a proposal to cut taxes across the board in order to provide a "Brexit bonus" for every Brit.
Mr Rees-Mogg told the Mail on Sunday the document was an "early draft" and insisted "there is nothing to be concerned about" in quitting the EU without a deal with Brussels.
But Lib Dem MP Layla Moran, a backer of the pro-EU Best for Britain campaign, said: "These hardline Brexiteers are buffoons.
"They've sat round a table and decided that, due to Brexit, we need to create a Star Wars-style missile shield.
"Reagan suggested this madcap scheme in the 1980's and was laughed at by everyone – yet these people want to resuscitate the scheme!
"What worries me is this right-wing cabal are the group that are holding the Government to ransom."
May's charm offensive as she wines and dines Tory MPs
THERESA May is planning to wine and dine dozens of Tory MPs to try and convince them to back her Brexit blueprint.
The PM is hosting backbenchers at 10 Downing Street in coming weeks as she launches a new charm offensive.
Mrs May wants to win over the "silent majority" of MPs who neither support nor oppose her Chequers proposals.
No10 aides believe that the hardcore Brexiteers who will never back chequers represent only a small number of backbenchers who will be outweighed by loyalists.
A source told the Sunday Express Mrs May's dinners were "an opportunity for the Conservative MPs to discuss the Government's detailed plans for leaving the EU and the opportunities ahead for the country".
They will be funded by the Conservative party rather than Government coffers.
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