If they are indeed the usual cypresses (either Leyland Cypress - Wikipedia, the free encyclopedia or something similar), they are very shallow rooted and the stumps can be pulled out with a winch. But you have to leave a decent stump, 6 feet or so, for the chain to be attached to and to get leverage.

Some friends removed a row of well established leylandii themselves and hired a winch to pull out the stumps, but they weren't quite as big as the ones you are talking about, probably 8m. With the ones you are talking about, first stage would probably be to rope yourself about 8m up the tree to cut the tops off, which I can imagine most people wanting to leave to the professionals.