Davos tends to turn the hardest of heads. During the annual meetings, where businesses pay big bucks to rub shoulders with political leaders and thinkers, a contagious aura of smugness fills this Alpine valley like a fog, killing much sense of reality.

Politicians need a quick corridor story to sell their country's virtues, and David Cameron has landed on a peculiarly ill-informed one. Most narratives are falsifiable only with the passage of time, but Cameron's story is demonstrably a fairytale right now.

The Cameron song is that Britain is going to be "re-shoring" businesses – the opposite of offshoring – in part because of cheap gas as fracking takes off: prices will fall as they have in the US, where they are just a third of Europe's prices. British consumers, whose bills will be halved, will doff their caps to Tory ministers who made possible this revolution of cheap energy. Grateful billionaires will come gambolling back to bring new business to Bradford and Bolton.

This is not a vision but a fantasy. Britain's geology has not yet been proved as suitable for fracking. Poland underwent a frenzy of over-excited hype about its shale gas deposits, only to be cruelly disappointed by the detailed geology. The same may happen here.

Assume, however, that our shale deposits are frackable. The second problem is that we have eight times as many people per square mile as the US, and those pin-striped protesters in Balcombe, Sussex, are rather more likely to notice the lorry traffic needed to supply a big shale gas pad than the good folk of Oklahoma.

Those irate British nimbys, along with the green groups who want to leave fossil fuels in the ground, are quite capable of making life miserable for the shale prospectors. They have to get planning permission, and then face tricks such as buying up tiny strips of land and claiming trespass.

In the US you drive by signs saying "Top dollar paid for gas rights". Companies can buy from residents who own the mineral rights under their own land. In the UK, mineral rights were nationalised during the first world war so people have little incentive to back exploration.

Another problem is that shale has particularly taken off in low-regulation US states, but thankfully it is unlikely that the UK will want to relax environmental safeguards such as protecting the water table. UK politics is much more like that of New York or New Jersey – both of which have declared moratoriums on shale – than Texas or Louisiana. High environmental standards, combined with planning controls, will inevitably slow down shale gas output.

Never mind my judgment, consider what the great god of the marketplace thinks of the prime minister's vision. There is a very obvious way of telling, because a company quoted on the Australian stock exchange called AJ Lucas owns 42% of Cuadrilla, one of the most active UK shale gas explorers. Its shares are still just a quarter of what they were worth in 2009.

Let us nevertheless suspend our disbelief, and assume that our brave frackers triumph over all these adversities and succeed in producing such vast volumes of natural gas that we once again become a net exporter of gas to other countries, as we were until 2004 from the North Sea. This is the nirvana that Cameron believes will cause re-shoring because our energy prices will be so low.

However, there is a little snag with the prime minister's logic. We have so many pipelines connecting us to the continent that if the price were lower here, some gas trader would buy in Britain and export it. Soon the prices would be virtually the same. For exactly this reason, energy prices were no lower than Germany's even when we were self-sufficient.

The reason they are lower in the US is because the shale gas revolution has happened more quickly than investors could build export terminals, and the gas has been trapped in the home market, driving down the price. Even when the terminals are built, the price will be substantially lower because of the very high shipping costs from North America.

There is a final devastating flaw in Cameron's argument. Imagine that we are once again afloat on a jet-black sea of fossil fuels: our energy prices may not be lower, but our balance of payments will benefit enormously from lower oil and gas imports; as a result, sterling is likely to become a more attractive currency to buy – a "petro-currency".

Then we would suffer from what used to be called the Dutch disease. The currency would strengthen, hitting trading businesses. In the 80s, offshoring began in earnest when we sharply increased oil and gas output. In other words, if the prime minister's fantasy actually happened, the consequences would be the exact opposite of what he supposes.

To sum up, shale may not happen. If it does, it will be slow. Even if it is eventually massive, prices will not drop. British industry, far from re-shoring, will be squeezed by the strong pound. Could the prime minister please hire a respectable economic adviser with a memory?