On my commuter train into London, the conductor – think Ann Widdecombe on a bad day – recently took it into her head to order any passengers who were standing to sit down.

“Will all passengers sit down for their own safety,” Widdecombe barked. “Now! I’ve told you once already.”

Passengers often stand for the very sensible reason that there are no seats; but that day, by some miracle, there were still some spare in the middle of the rows of three. The standing rebels didn’t budge.

“It’s the rules, so sit down!” screeched Widdecombe.

“You’ve made your point,” replied one long-suffering passenger. “Now do shut up.”

The problem was clear. Through deluded design, the modern trains on my line into Waterloo have seats built for slimline Victorians, not the fatties of the 21st century. Anyone of large build who tries to sit in a middle seat ends up with a buttock perched on the thigh of the person either side. Some people might pay £3,000 a year for such thrills, but most commuters prefer to have just a tiny bit of personal space as they head for work or home.

That shambles sums up the state of Britain’s rail network: it is trying to cram too many people into too little space.

Rail is in the midst of a huge and unexpected boom. Since 1997, demand has soared 45%. Trains are carrying more passengers than in the heyday of steam, when the network was twice as large.

On some routes trains are carrying 50% more passengers than they were designed to do – and overcrowding is so bad that it would be illegal under European Union law to transport animals in such conditions. Why don’t passengers riot? Because they’re packed in too tight to move.

To solve such problems Network Rail, the body responsible for the tracks but not the trains, announced last week that it was studying the feasibility of building five new high-speed rail lines.

Oh whoopee-do, thought many commuters. High-speed conjures up images of trains bulleting across Europe in half an hour – but what use is that if you just want to get from Surbiton to Waterloo without suffering asphyxiation?

The Network Rail argument is that new high-speed lines would both provide a faster inter-city service and free up space on lines for more commuter services. There is some merit to this, says Stephen Joseph, director of the Campaign for Better Transport.

“Overcrowding is endemic,” he says. “The main lines out of London are going to run out of capacity within 10 years. If you are going to build new capacity, you might as well build it to take high-speed trains.”

According to Joseph, the cost of high-speed rail lines compares favourably with new roads or widening existing ones. Atkins, an engineering consultancy, recently produced a study arguing that the economic benefits of high-speed rail would outweigh the expense. A west coast line, it said, would cost £9 billion and produce benefits of £15 billion; one on the east coast would cost £12 billion and produce benefits of £29 billion.

High-speed lines could also take the pressure off Heathrow, by attracting passengers who now fly between cities such as London, Birmingham and Manchester.

It all sounds splendid, the sort of grand transport vision that has sadly been lacking in the past. There are, however, drawbacks, especially for commuters in the southeast.

None of the proposed high-speed lines goes south of London. It’ll still be sardines all the way to Surbiton and beyond. That’s one reason why Tim Leunig, an independent expert on rail at the London School of Economics, is less than enamoured of high-speed plans.

“They would be a complete waste of money,” he says. Leunig argues that high-speed rail is fine for traffic between very large urban centres, such as London and Paris, but of little use in solving Britain’s capacity problem.

“We need to get back to thinking about what our railway is for,” he says. He notes that “about 70% of rail journeys begin or end in London, and the three busiest stations are Waterloo, Victoria and Liverpool Street”.

In 2006-7 Waterloo, serving the south, had 84m “entries and exits”, Victoria 67m and Liverpool Street 55m, compared with 14m at Manchester Piccadilly and 14m at Birmingham New Street.

Rail planners, says Leunig, are trapped in the old romance of fast, long-distance travel; but the reality is that modern rail travel is concentrated around London, especially commuting in the southeast.

Leunig thinks there should be a new line running north-south under London. It could increase capacity in the south, link Waterloo, the City and Liverpool Street, and perhaps run on to Stansted. It might also help ease congestion on the London Underground, which carries almost as many passengers as the entire rail network.

None of this will happen any time soon, however. Instead, for the next five years the government hopes to ease the immediate congestion by tweaking timetables and making trains longer. Better than nothing but it will do little more than keep up with the predicted growth in traffic.

The problem is so acute that Leunig has another radical idea. “You could reintroduce a third class, with standing only,” he says. “You can fit in a lot more people standing up than sitting down.”

He suggests ripping seats out of some carriages and offering very cheap fares to those prepared to stand. At least they wouldn’t be told to sit down.

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