I'll bite. How ?
Public ownership surely means its funded by the taxpayer and private ownership means the cost is funded through the ticket price.
In theory all state ownership would mean is the £200m of dividends taken by shareholders would instead be taken by the taxpayer.
In reality it's more complex than that - especially if the government uses the railway for it's own ends (like lowering season ticket prices for 'hard working commuters'), and that's before the cost of capital.
However no matter who owns the rail, it's still possible to have an extra train self funding. For example, if there are currently 200 people who refuse to travel because the train is overcrowded, and they would pay £150 each for the trip, another train would mean that's an extra £30,000 of revenue.
You'd have to work out the cost of that train over the course of a year, the actual number of people currently not travelling or travelling by other means, the diagramming to ensure it's in place, etc, but if the railway can't run a train that earns say £10,000 an hour in revenue 18 hours a day 5 days a week without making a loss, then perhaps it deserves to die?