Nick Hudson from the Holmes Place Training Academy replies:
Firstly I would suggest you need to find out why your knees hurt and probably see a physiotherapist to ensure you don't have muscular imbalances that might cause further damage through running.

Cycling will certainly keep your heart strong, though unfortunately, due to 'the rule of specificity' there isn't a good carry over in fitness from cycling to running. Runners may use other cardiovascular activities such as cycling as a form of 'active recovery' when they want to avoid overtraining, but as the main method to improve running fitness, it won't be very beneficial.