The Treasury has refused to fork out for the proposed link, which was described as the “world’s most stupid tunnel” by the Prime Minister’s former chief adviser Dominic Cummings.
The project was being considered by a transport connectivity review led by the Network Rail chair, Sir Peter Hendy.
However, The Scotsman understands it will be kept under review in case technology advances in the future to make it more feasible.
A UK Government source explained: “The idea of the tunnel is a good one in terms of the strategic network. It’s doable, but eye-wateringly expensive.
“It would cost £100 billion, considerably more than was first expected.
“We will keep it under review, as advances in technology could make it more attractive in the years to come.”
Another government official told the Financial Times: “It’s dead – at least for now.”
The issues are understood to be over the distance being too far to let people drive, meaning it would have to be rail, a shallow gradient, as well as problems over having to go around Beaufort's Dyke.
Despite the plans being axed, the planned improvements to the roads approaching where the tunnel would have been will go ahead, with Sir Peter’s report expected to be published towards the end of October.
The UK Government source criticised the Scottish Government’s continuing refusal to engage with the review, saying they were ignoring available funding and claiming it was a “power grab”.
The source added: “There remains a need to improve links to Northern Ireland.
“The A77 and A75 are important. For us the A75 is a very good illustration of why you need that UK strategic transport network.”
A UK government spokesperson added: “Boosting connectivity across the UK and improving transport infrastructure are at the heart of our levelling up agenda.
“That is why we asked Sir Peter Hendy to lead a Union Connectivity Review to look at future transport priorities, based on the wider strategic case for investment and the benefit it will bring to people and businesses across the UK.
“On the back of his interim report in March, we have committed £20 million to develop plans that can assess options on road and rail schemes.
"We’re now looking forward to his final recommendations ahead of the Spending Review, where we will consider and confirm funding plans for delivering improved connectivity between all parts of the UK.”
Mr Johnson’s former communications director Guto Harri last month insisted a “Boris Bridge” should not be dismissed entirely.
He explained: “He wants to maintain the Union and he wants to persuade the rest of the world that we’re still big players and can build big things — and what would be bigger than a tunnel under the Irish Sea, linking Scotland and Northern Ireland?”.
A Scottish Government spokesperson said: “The Scottish Government has not investigated or undertaken any feasibility for a fixed link between Scotland and Northern Ireland and has no current plans to do so.
“Transport Scotland are currently undertaking the second Strategic Transport Projects Review, which will inform the Scottish Government’s future transport investment priorities.”