What do you mean by infrastructure? Tracks and stations are administered by Network Rail, which is publicly owned.
Think at least some stations are being run by the train operators? For example Chester station is run by TfW afaik.
What I mean with running the infrastructure down is that there has been a lack of investment for keeping tracks in prime condition. I don't think there is any incentive for Network rail - if the trains can't run properly, they'll blame the train operators. And the train operators blame Network rail. I think it's a general problem, rail tracks are fairly robust, so for a while, not much needed to be done, so money was spent elsewhere. But now they are old, and need repairing/replacing more regularly, and there's no funding for it. There is also a lack of interest - network rail just blame the train operators, and the train operators blame the state of the tracks.
Also I think the definition of "value" has changed. Countries like Britain and Germany used to be proud of their railway. Investment went into it with a sense of pride of the great national infrastructure (same as the NHS, hah!). Now everything has to measured with regards to the profit it brings.