This one will take some magicking.
The main road through Bruton is the A356, which goes from Nunnery Catch to Yeovil. The closest station to the Yeovil end is Yeovil Pen Mill, and the closest to the Nunnery end is Frome. The fastest direct service between these stations is the GWR service which takes 29 minutes (for example, 0909 Gloucester to Weymouth calls at Frome 1101 (dep 1102), Bruton 1113, Castle Cary 1118, YPM 1131).
Over the network, there are various combinations of direct services with 29 minutes of call between various stations. But we're going to look at Accrington to Hebden Bridge (On the Northern 0718 out of Blackpool, it's Accrington 0811 (dep 0813), Burnley Manchester Road 0821, Hebden Bridge 0842). The A646 connects these settlements (with a small section of A679 at the Accrington end).
For a good part of the A646, the River Calder flows alongside it. This river runs east between Bradford and Huddersfield, through Wakefield, and merges into the River Aire, which itself merges into the Ouse flowing into the Humber. This last occurs at a place named Faxfleet.
Along the A646 we find a small village named Holme Chapel. This has three letters in common with Faxfleet (one l, two e's). Bruton also has three letters in common with Burnham.
Therefore, the commonality of Holme Chapel with Bruton is that both are on a main road whose two ends take 29 minutes to travel by rail at the fastest, with a river flowing through them which reaches the sea at a conurbation which shares three letters with the name.
Dammit. Doubleposted again.
Sherbourne has a skate park, and the A30 runs through it. It has a population of 10365. Another town on the A30 with a similar population and a skate park is Hook in Hampshire (9060).