Nearly. Her complaint that “half of people living in rural areas, and so many small businesses, can’t get a decent broadband connection” is probably based on a report produced by the regulator Ofcom last year, which is now a little out of date. Ofcom found 1.5m rural premises – about half of the total – could not get the basic speed needed to watch video and support multiple devices such as tablets, phones and smart TVs. The regulator said it would be another three years before all these premises get the 10 megabits per second (Mbps) it considers a minimum for modern users.

Things have improved since then, thanks to the taxpayer-funded BDUK scheme to wire up the countryside. The total suffering from slow connections has fallen to 25% across all rural areas, though half of those living in hamlets are still below 10Mbps. Business parks have also complained of being left out.

Ofcom said last year that only 68% of small and medium-sized businesses have superfast, with some 400,000 still waiting. The problem is not confined to rural areas. BT’s superfast broadband roll-out, which has now reached 90% of all homes and businesses, is bypassing those living in tall buildings – from council tower blocks to highrise luxury flats.

How is the UK doing compared to other countries?

Not too badly – for now. The average customer can download at a rate of 15Mbps, which means the UK ranks 20th in the global speed league. But much smaller economies such as Bulgaria, Romania and Belgium are already faster. South Korea is at the top of the pile, with 27Mbps, and Norway is in second place with 20Mbps.

The concern is that, having finished the bulk of its superfast upgrade, BT does not have sufficiently ambitious plans for the future. Homes are still connected to street cabinets by copper wires. The company plans to extend fibre-optic cables closer to its customers’ doorsteps, using a technology called G.Fast, but copper will still be used for the final stretch. BT claims G.Fast will deliver speeds of up to 300Mbps, which is more than most users need for now. But experts say the only future-proof network is one that uses fiber cables only, all the way from the exchange to the premises.

Fiber to the premises, or FTTP in telecoms jargon, is at least three times as fast and would ensure no fall in speeds at peak times. BT and Virgin Media, the two biggest network operators, plan to connect a mere 3m premises between them using FTTP. To be fair, BT says it will fill the gaps in its superfast roll-out by focusing on tall buildings, business parks and high streets. But other countries, including China, France, Portugal and New Zealand, have much bigger plans.

What would improve broadband?

Rivals say BT needs to split off its infrastructure division, Openreach, into a separate company. More than 560 TV and broadband resellers, including Sky and TalkTalk, rent their lines from BT. And these resellers say they receive a poor service, with engineers taking too long to fix faults and install new lines.

In July, MPs concluded that BT was “significantly under-investing” in Openreach, to the tune of hundreds of millions of pounds a year. Funds that should be going into broadband were instead being spent on football rights designed to boost the newly launched BT Sports channels. A top-class TV service is part of BT’s strategy to stop its customers defecting to other providers.

Since BT started competing with Sky for live football, the amount collected by clubs each season has rocketed from £594m to £1.7bn. BT counters that it spends less on football than on fiber – this year it will invest £1.4bn in its network, and last year it spent £544m on sports rights.

What are the practical hurdles?

BT chief executive Gavin Patterson has threatened 10 years of litigation and a halt on network investment if the government forces through structural separation.

The BT pension scheme is a big obstacle. The largest occupational scheme in the country, its deficit stands at almost £10bn. Splitting the commitment would be a complicated and expensive business. Ofcom is proposing a middle way: legal separation. Openreach would get a board of its own, with control over budget, ownership of the network and a directly employed workforce. If this still doesn’t work, Ofcom boss Sharon White says “we would return to the option of full separation”.

Is Theresa May serious about sorting rural broadband?

Time will tell. Ofcom’s proposals for legal separation were published at the end of July, just a couple of weeks after the new Conservative leader moved into 10 Downing Street. The prime minister has not had a chance to put her own stamp on the strategy, but her keynote gave no clue as to whether she will push for a stronger remedy.

Is infrastructure spending the answer and will it happen?

Labour thinks so. It has promised to raise £500bn for investment in infrastructure, including broadband. The chancellor, Philip Hammond, last week made a more cautious case, for “very carefully for targeted, high-value investment in our economic infrastructure”. Other governments are spending in this area. Singapore has already connected every home to fiber, although in a 720 sq km city state, this was a fairly straightforward task.

In Australia, the job of wiring vast expanses of outback required special measures. Structural separation was forced on the Telstra network in a negotiation that took five years. The government committed A$30bn to fitting FTTP to 93% of homes.

Initiated under a Labour administration, the project has since been scaled back. Estimates for the cost of a national all-fiber network in the UK vary from £25bn to more than £50bn. That kind of money could probably not come from the private sector alone.