Are there any good trails / bridleways around there ? Please ridden a bit further towards minehead

Head north to Dunkery Beacon and Horner woods. Plenty of trails thataway.
OS of the area is your friend for linking BWs.
I used to visit friends in Withypool quite often and would just link lots of likely looking tracks using http://www.bikehike.co.uk

There is a loop around it close to the waters edge but it’s a bit dull with very little elevation change over 7 miles.
Head over to Dulverton, plenty of good stuff North & West out of the town.

Good for the kids. Tiny bit of stuff on Hartland but you’re better on Exmoor and around there really.

Thanks ile have a look on os maps and plan a route.