The most shocking admission made by Heidi Alexander, the new transport secretary, was that the pay increase for train drivers awarded by her predecessor Louise Haigh resulted in fewer staff being available – because they could afford to work less overtime.

In other words, the Labour government inherited a railway system in a terrible state and managed to pay more to make it worse. This is not a good start.

The Independent’s transport correspondent Simon Calder provides a magisterial overview of the state of play: in return for an annual subsidy of £12.5bn, 100,000 trains were cancelled in the third quarter of last year, and of those that ran, one in three arrived late. Despite the generous award that settled the strikes in progress at the time of the election, industrial relations have remained poor, with more walkouts planned.

In addition, the network is plagued with mechanical problems and staff shortages.

All this has been true for some time, and Labour is entitled to say, as a spokesperson for the Department for Transport told The Independent, that “it will take time” to put right. But the new government has started off in the wrong direction.

Just look at the statement provided to us by the DfT^» (Department for Transport - about) spokesperson. After saying how bad its inheritance is and how it will take time to fix it, it said: “We are determined to set up Great British Railways.” What the railways need is not another renaming exercise.

It went on to boast about “our flagship public ownership bill”. But public ownership is no magic solution. State-run Northern Rail cancelled 142 trains a day on average last month. Of the services that did run, nearly half arrived late.

Then the DfT statement talked about “reforming the overcomplicated fares system”. Yes, it is confusing, but it is not a fundamental problem.

And finally, it said: “Our number one priority is to provide passengers with the reliable, accessible, and more affordable services they deserve.” Well, those are three priorities, and if you have too many priorities then nothing is a priority. Especially if the third – cheaper tickets – potentially contradicts the other two.

If Ms Alexander is to break the cycle of loss of confidence in the railways leading to higher subsidies, she needs to set a single priority and pursue it with steely purpose. The only thing that matters is to make rail services reliable again. If she can cut cancellations and late running, everything else will fall into place.

But to do that she has to strike a historic bargain with rail workers. Drivers in particular are paid well, but in return, they have to work in ways that serve the people who pay their wages – their passengers.

This will in turn require her to tell some blunt truths. One is that the unions will damage their members’ livelihoods if they continue to drive people away from the railways, losing revenue and undermining the case for subsidy. The other related point is that the case for subsidy is weak, and that passengers must be prepared to pay more.

The blunt part of that message is that half of the population uses railways less often than once every six months – and the half that uses them most tends to be better off.

The more palatable part of the message, however, is that if Ms Alexander can make the trains run on time, more people will use the railways and there will be less need for subsidy. If she can deliver that virtuous circle, after Labour’s false start, it would be a historic achievement.