In a statement published on the Medium website, the younger Johnson claimed the Brexit deal the Prime Minister is pushing for would leave the United Kingdom "economically weakened, with no say in the European Union rules it must follow and years of uncertainty for business".
On Friday the DUP, whose support Theresa May relies on for votes in the Commons, said they can not support any deal which included the possibility that Northern Ireland would be treated differently from the rest of the UK.
However, there are concerns that a second referendum could embolden the far-right in the United Kingdom, while Eurosceptics point to examples where votes within EU member states rejecting greater federalism and austerity have been overturned in what they say is yet more evidence that there is a "democrat deficit" within the union.
To give the public a choice between these two disastrous versions of Brexit would be a "failure of British statecraft on a scale unseen since the Suez crisis", he said, referencing the 1956 conflict against Egyptian President Gamal Abdel Nasser that is widely seen as marking the moment at which Britain formally lost its imperial role in the world. This is a con on the British people. "If these negotiations have achieved little else, they have at least united us in fraternal dismay", he said.
Until now the focus has been on the Conservative Brexiteers who have pledged to vote against the compromise deal being negotiated in Brussels.
"Now is the time for people to stand up for what they believe in or we will sleepwalk to a Brexit disaster".
He wrote: "Boundless admiration as ever for my brother Jo".
When May was presented with the alternate proposal, she told the ministers that their plan "was not needed yet" but it was greeted with a "surprisingly warm response" from Finance Minister Philip Hammond, the Sun said.
She has consistently rejected the idea of another nationwide vote on Brexit, insisting her obligation is to make good on the will of the people as expressed in 2016.
Eloise Todd, head of the anti-Brexit campaign group Best for Britain, said: "This is an incredibly courageous move from Jo Johnson at a time when the public desperately needs more MPs to act in the national interest". "We know a General Election is their first choice, question becomes what is their second choice - exit or referendum".
"The prime minister thanks Jo Johnson for his work in government".