Several other London projects have received funding, including Core Arts in Hackney (£27,000), Herne Hill Velodrome (£11,420) and Brixton BMX Track (£15,000).
British Cycling, which runs the scheme with Sport England and DCMS, says a further £30m would allow the creation of 250 new community cycling spaces.
Clancy, a former Team GB Olympian, said accessible facilities were essential in a busy city where many beginners may be reluctant to ride on the road.
“It’s really important that people have a safe and accessible place to ride,” he said.
“If beginner cyclists, children in particular, are not confident and able to go out on to the roads, they need places to get on the bikes.
“I appreciate there’s always asks for budget and money from the government, but it seems to be money well spent and there is a 1 to 6.5 return on investment.”