QUEEN ELIZABETH gamely saluted “la combinaison de l’élan français et du pragmatisme britannique”. President François Mitterand countered with a courteous nod to Britain’s help in two world wars. A centuries-old dream of connecting Britain to France was formally realised on May 6th 1994 with the opening of Eurotunnel under the English Channel, la Manche.

But the project, so inspiring on the drawing board, was a nightmare on (and under) the ground. It cost twice as much to build as budgeted. Even 20 years on, only half as many people use it as were expected to. A first dividend to shareholders, promised in 1995, was paid in 2009. By that point the 750,000 investors, mainly French, who poured their savings into shares had seen most of them vanish in the restructuring of Eurotunnel’s unpayable debt in 2007.

Slowly, however, Eurotunnel is coming good. As Britain’s economy grows, it is pulling the company up. In 2013, 20.4m people used the tunnel, either in their own vehicles aboard the tunnel shuttle or as passengers on Eurostar’s high-speed trains. The year before it was 19.9m. Rail freight increased, too. Revenues in 2013, at €1.1 billion ($1.5 billion), were 12% higher than in 2012. Next year Eurotunnel, which is headquartered in Paris, may begin to pay French corporate-profits taxes.

Even now, the tunnel is operating at only a bit over half of its capacity. But the next two decades are likely to transform it from a useful bilateral link into a thoroughfare through which the rest of Europe can travel. The reason is more competition.

The European Commission is keen to open rail infrastructure to train operators from all member states. That is already happening in freight, with companies from various countries running trains through the tunnel. Eurotunnel is cutting its freight charges from June after the commission threatened to go to court, so volumes should increase. But passenger travel has been reserved for the high-speed trains operated by Eurostar, which is 55% owned by France’s state rail operator, SNCF. Britain owns 40% (though the government is thinking of selling) and Belgium has 5%. That monopoly is about to end.

Deutsche Bahn, the German rail company and SNCF’s great rival, has been agitating for years to run its trains through the tunnel, connecting London with Germany and the Netherlands. In June 2013, after serious nudging from the commission, Britain and France, which formally supervise Eurotunnel, said it could. Delays in getting new rolling stock from Siemens have pushed back the date of Deutsche Bahn’s likely tunnel debut. Eurostar itself is not standing still. It has tested connecting London with Lyon and the south of France and announced plans to extend the network to Marseille and Amsterdam. Other countries’ operators will soon join in.

Dieter Helm of Oxford University says it is time to scrap Eurostar’s monopoly. The important thing with infrastructure, he thinks, is to keep tracks, networks, pipelines and so on separate from the stuff that goes through them to allow competition to lower prices and improve service. As Eurotunnel opens up to new operators, he says, “over the next 20-30 years it only needs a little imagination to think you will be able to get on a train in any city in Europe and go to any other city.” Imagination, and a big whack of investment.