Tarka Trail, Devon
Another disused railway line (thanks, Dr Beeching!) forms the basis of the Tarka Trail from Braunton to Meeth. At 31 miles, families might prefer to stick to the start of the trail along the river Taw, one of Tarka the Otter's rivers.
Details www.sustrans.org.uk; bike hire available from Barnstaple railway station from March to October (www.tarkabikes.co.uk)