Engineering experts have poured cold water over Boris Johnson’s “bonkers” plan to build a bridge between Scotland and Northern Ireland for £15bn.

The prime minister – who first touted the idea of the 20-mile-plus bridge last year – put a price on his proposal for the first time last week, saying it would “only” cost the multibillion pound sum.

But experts have said that, while it might technically be possible to construct the bridge connecting Scotland’s mainland with the outskirts of Belfast, it is potentially fraught with problems and the costs could spiral.

One eminent engineer, who was behind London’s Millennium bridge, told the Guardian it was “bonkers” to put a price on the plan before a proper design was in place. Another engineering academic labelled the proposal “dubious economics”.

It comes after leaked documents emerged on Tuesday that revealed that Johnson had ordered government officials to explore the possibility of building the bridge. On Thursday, during a visit, the prime minister told schoolchildren: “[I was talking yesterday] about building a bridge from Stranraer in Scotland to Larne in Northern Ireland – that would be very good. It would only cost about £15bn.”

Johnson first floated the idea in an interview last year, saying: “What we need to do is build a bridge between our islands. Why don’t we? Why don’t we?”

But his proposal drew criticism then, with one retired engineer comparing the feasibility of the plan to “building a bridge to the moon”.

James Duncan, from Edinburgh, raised concerns over the practicality of constructing a bridge across the “stormy” stretch of water – more than 1,000ft deep in places – which would require dozens of support towers at heights “never achieved anywhere in the world”. Bridge builders would also have to navigate Beaufort’s Dyke, a submarine trench in which the Ministry of Defence dumped more than 1m tonnes of obsolete munitions following the end of the second world war.

Chris Wise, the engineering designer of the 2012 Olympic velodrome, said he supported the principle of connecting the two countries but raised a series of question marks over the practicality of the proposal. “It’s socially admirable but technically clueless,” he told the Guardian. “If Boris wants to stay prime minister he needs to stop promising figures before he can deliver them.”

Wise, the engineering director behind London’s Millennium bridge, explained: “Technically, there’s a solution which is to build something in dry dock, tow it out, sink it into position. But when you’re talking about something that is going to be the same height as the Eiffel Tower before you even get to sea level that’s a major, major beast.

“It probably means you’re not going to be putting any supports in there [to hold up the bridge] so then the question is whether the span you’re left with is something that is plausible. Because the biggest bridges in the world are only a mile, or a mile and a bit long for an individual span [without a support].”

Similar bridges have a series of supports to hold the structure in place. They include the 4.8-mile Øresund bridge, which connects Sweden to Denmark.

Wise said he was also concerned by the optimistic £15bn price tag. “If everything from the Olympics to HS2 are anything to go by, to quote the number and the price of any of these publicly funded projects this early without a design, in my view, is bonkers,” he said.

“You don’t know what something is going to cost until you know what you’re going to build. So unless Boris is sitting on a design that nobody else knows about, which he may be, I think it’s a bit foolhardy to put a price in the public domain. They always go up, they never go down. But it sounds cheap to me.”

Dr John McKinley, a senior lecturer in environmental engineering at Queen’s University Belfast, also raised doubts. “Like a lot of infrastructure questions, a bridge or tunnel across the Irish Sea is feasible engineering but dubious economics,” he said.

“The idea has been floating around since the 1880s and seems to come around every 30 to 40 years. The shortest distance would connect Northern Ireland and Scotland, but that involves going through Beaufort’s Dyke, a 200- to 300-metre deep channel in the middle of the Irish Sea.

“For a bridge, you would need support piers more or less equal in size to the largest civil engineers have built so far. For a tunnel the underwater part would either be about three times the length of that for the Channel tunnel or go about four times as deep. Connecting Belfast to Glasgow, lovely places though I think they both are, isn’t as obviously a good thing as connecting London to Paris.”

David Barwell, the UK and Ireland CEO of AECOM – one of the world’s biggest engineering firms – said: “Engineers, we can come up with any which way you want to get something like this done. You can do it … there would be an engineering solution. I think the next piece, the other piece which people are asking is, ‘OK, well there’s an engineering solution, but at what cost?’”

Asked whether he thought the project could be completed for £15bn, he said: “I really don’t know. The problem is, it’s always dangerous talking numbers at an early stage in the project.”

A government spokeswoman said: “The prime minister has often spoken about his support for infrastructure projects that increase connectivity for people and particularly those that strengthen the union. As you’d expect, the government regularly commissions work to examine the feasibility of potential projects.”