A National Trust 'advertorial' appeared on The Guardian website recently, setting out the organization's stall on cycling. The Wandle Trail goes through Morden Hall Park in Merton, which is the nicest cycle path in the borough (not that competition for that crown is very intense). The Trust is developing mountain biking facilities, and generally speaking is fairly cycling-friendly.
However, for a conservation organization it has a pretty poor record on car dependency. When you join the National Trust, you get free car parking. There is no discounted rate for those who don't use a car. At most National Trust sites, there are massive car parks with staff in attendance. Realistically of course, most people will come by car, but it's somewhat disappointing that the organization is not giving more incentives to visitors to leave their cars at home.