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The Wandle Trail is a 12.5-mile (20 km) walking and cycling trail that follows the River Wandle from Croydon to Wandsworth in south-west London.

When fully open this cycleway will go between the River Thames at Wandsworth to Brighton via redhill and Crawley
Website: Link
wikipedia; Link

National Cycle Network route 20 will, once completed, link Wandsworth in south London with Brighton. It will be 45 miles long. The sections between Wandsworth and Carshalton, and between Crawley and Brighton, are already completed.

More information is avaialble from Sustrans: Link

The National Cycle Network is a network of cycle routes. It was created by the charity Sustrans Link (Sustainable Transport), aided by a National Lottery grant.

Many routes aim to minimise contact with motor traffic, though 70% of them are on roads. In some cases the NCN uses pedestrian routes, disused railways, minor roads, canal towpaths, or traffic-calmed routes in towns and cities.