I followed the NHS maternity cuts to the end. It's Northampton.

The maternity unit in one Lincolnshire town has four consultants on its rota. Two of them are the same person on different days. The NHS Alliance asked me to look at this. Its acute care director has warned that up to 20 units in England may have to shut so that births can happen where the doctors are.

I did what they asked. I ran the numbers all the way to the end. The end is one maternity unit. It is in Northampton, because Northampton is in the middle. Everyone in England gives birth there, on a Tuesday.

The sample was fourteen hospitals. The control group was fourteen hospitals we left alone. The difference was clear. The p-value was 0.03. That is the chance we got this result by luck. Three in a hundred. I would not bet a house on it, but I have bet a health service.

Tuesday was not a whim. Tuesdays are the quietest day on the motorways. Births already run to a clock in part, because of planned caesareans. We extended the clock. Babies not due on a Tuesday are asked to hold on for the next one. Our data suggest most will. The ones that will not are a small group, and we have a leaflet for them.

One finding keeps me awake. The vending machine on the Northampton ward stocks only salt and vinegar. We modelled the wait for cheese and onion. The queue reaches Leicester in the second month. By the fourth it reaches Sheffield. We have no plan for this. I want to be honest about that. It could end everything.

Dawn Prentice-Hale speaks for the NHS Alliance. She has read the study twice. "Change is always hard," she told me. "We know this is unpopular. But a baby born in a clean, fully staffed unit two hundred miles away is safer than a baby born in a well staffed unit nearby, if the nearby unit does not exist. Which it will not."

Keira Mottram is expecting her second child in Carlisle. She has worked out the drive. "It is five hours if the A1 is kind. It is not usually kind. My first came in forty minutes. I have been told to leave on the Sunday."

The study did not look at outcomes for mothers. It looked at outcomes for rotas. Rotas did very well.

I should hedge. I always hedge. We measured whether the doctors could be in one room. They can. We did not measure whether the mothers could. That is a second study, and the funding has not come through.

The NHS Alliance has not accepted the Tuesday finding yet. It says it is considering twenty closures for now. I told them twenty is a stop on the way, not a destination. They said that is a political problem. I said politics was outside my sample. We left it there.