Bring a saucepan of slightly salted water to the boil and add the broccoli. Cook over a high heat for 3-4 minutes, or until quite tender, then drain.
Melt the butter in a frying pan over a medium heat, add the leeks and cook for two minutes, then add the cooked broccoli and cook for a further two minutes.
Add the cream and simmer for two minutes, then add the cooked linguine and Stilton and mix together well.
To serve, spoon the pasta mixture into a serving bowl.