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TrainTimes already has a map (http://traintimes.org.uk/map/#bhm) although I'm not sure of their data source.

I've looked at this before and it's already doable through the network rail api (https://datafeeds.networkrail.co.uk/), which differs from the national rail enquiries api and as far as I can remember (and can see) is free.

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Playing around with it, there is room for improvement in the accuracy. Quite a few routes and stations are missing.

Yeah definitely, Edinburgh has acquired a few extra rail bridges! IIRC the network rail movement feed tells you when a train has reaching specific passing points, so there is a very granular level of data available if you want to show movements on the track.

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