Coppicing is more productive than felling and replanting, since you are not wasting time while the tree produces a large root system.
Almost all native UK species can be coppiced, but for firewood you probably don't want to grow oak which needs a 50-year cycle between harvests!
Willow can be coppiced annually. Other popular "short period" trees are hazel and hornbeam, but those typically have a 7 year cycle between harvests. After that you are looking at species like sycamore with 15 years between harvests.
Birch can be coppiced on a 3 or 4 year cycle, but there is a risk of killing the trees so that may not be a good choice for you.
Willow is very easy to grow from cuttings. Just add lots of water. In fact virtually any lump of willow wood (even a slice cut from a large trunk) will start to grow roots if you simply leave it in a bucket of water for 6 or 8 weeks. For coppicing you want to plant the cuttings 12 to 18 inches apart, so over time they develop into a "forest" of vertical stems, not individual "trees".
There are two downsides to willow's growth habits. Don't leave "rubbish" lying no the ground after you harvest willow, or next year you will have small willow trees growing everywhere. The other issue is less easy to fix: don't grow willow anywhere near underground drainage pipes. The roots are notorious for finding a way into the drains to access the water, and then causing blockages and major structural damage.