From an initial glance at the problem it is clear that there are railway inconsistencies, such as Blandings Castle being on the Severn and in Shropshire, and yet one could get a train to its station from Paddington with a 'first stop at Swindon'.
I realised that I must discard certain data. I have tried to find a place which fits the main topographical data and which lies within the limits of the largest number of the railway facts.
The topographical data are as follows: the castle is in Shropshire; the Severn runs through its grounds; it is 45 minutes by car to Shrewsbury, not hurrying; the Wrekin is visible from its battlements; it is 2 1/2 miles or so from the castle to its station.
The full report can be found in the atlas.