Free broadband – indeed, an ultra-fast fibre service delivered to every household and business – sounds a highly popular idea. And Openreach, BT’s broadband division, is a deserving target for nationalisation, one could argue. The watchdog Ofcom has been regularly frustrated over the years by the company’s foot-dragging over the pace of fibre optic roll-out.

In 2017, Ofcom forced the legal separation of Openreach to raise the stakes and make the threat of a breakup of BT feel real. So why not go further by pressing the nationalisation button to ignite investment?

Well, the numbers also matter. The first challenge, as with all proposed nationalisations, is establishing the price to be paid for the assets. It will be done “in the usual way, with parliament setting the price”, said the shadow chancellor, John McDonnell, as if the definition of fair compensation is obvious. It’s not.

Openreach has a regulated asset base – one form of official valuation – of £13.5bn but its market value might be closer to £20bn, reckons the City. Pension funds are almost honour-bound to fight to protect savers’ interests. BT’s biggest shareholder, Deutsche Telekom, which owns 12%, also won’t want a few billion pounds of assumed value to slip between the nationalisation cracks.

The City thinks shareholders’ rights are strong. “The UK has bilateral investment treaties with countries in which overseas BT shareholders are located, and these are intended to protect against asset expropriation,” said the investment bank Jefferies. “UK-based shareholders might expect to receive equal treatment.”

That legal scrap would be resolved eventually, but the next problem would be how to compensate Virgin Media, the broadband parts of Sky and TalkTalk, and broadband-only specialists such as CityFibre. Those companies have been incentivised by Ofcom for years to lay their own fibre cables to compete with BT, but their businesses would implode if a new state-owned British Broadband were to give away the product for free.

McDonnell suggested British Broadband could negotiate access rights, or that the smaller rivals could be brought within the “ambit” of the publicly owned operator. If the latter means follow-on nationalisations, the upfront bill would clearly be bigger.

Then there’s the actual cost of building the new fibre network. McDonnell talked about £20bn but the BT chief executive, Philip Jansen, thinks the bill would be £30bn to £40bn, one of several disputes over the back-of-the-envelope arithmetic. While Labour referred to £230m of annual “running costs” for the new network, BT’s last accounts show operating costs of £2.6bn for Openreach. Estimates of maintenance costs for the current broadband network are put at close to £1bn a year.

If the higher figures are correct, how do you get the likes of Amazon, Facebook and Google to part-fund the policy via a digital tax, as Labour intends. One can see the moral case: the tech giants’ current UK tax contributions are disgracefully small. But extracting fair digital taxes from multinationals is not straightforward, as governments everywhere know. Discussions at the Organisation for Economic Cooperation and Development on this subject grind on.

Then there’s the deficit in BT’s pension fund – £6bn at the last count. That complication was one reason why Ofcom opted not to break up BT in 2017, but nationalisation of Openreach would bring the issue to the fore again. Someone has to fund the scheme and Openreach’s current £5bn of annual revenues won’t survive if broadband becomes free.

At the ballot box, financial details may count for little. Labour’s nationalisation policies for water, the energy networks, and Royal Mail are said to be popular. Free broadband might enjoy even better reviews – the idea will certainly stir more debate than the right ownership structure for electricity pylons, one suspects.

And McDonnell is clearly correct when he says the UK lags behind many other major economies on access to ultra-fast broadband. It would be hard, though, to describe his plan as detailed. There are a lot of unanswered practical questions.