The Norfolk Broads:
A bit further afield, but definitely worth the trip! Norfolk is possibly most famous for the man-made Broads, a National Park with over 125 miles of navigable lock-free waterways set in beautiful countryside and studded with charming and picturesque towns and villages. Loads of options to hire a boat for the day or go on a sightseeing guided tour, you can cruise the waterways and enjoy the scenery and wildlife that surrounds you. Dogs welcome too. More more info see here.
38 miles (c.1 hour drive) from West Heath to Wroxham NR12 8RX