Livestock
Chickens are great. Almost everyone has room for some chickens. They eat leftovers and can lay an egg a day from a few months old until they are about six years old. If you are interested in keeping chickens try wandering down to your local allotments, find someone who keeps chickens and ask them where they bought the chicks. The www.poultryclub.org is a good source of advice too.
Chickens don’t need much room especially if you let them out once a day
Goats
One goat will give you enough milk to supply on person with milk, butter and cheese. On the negative side they will eat anything but should not be fed everything. Their main food is grass but during the winter they will need hay or silage and that can be expensive if you haven’t got an acre per goat.
Pigs
These are a bigger step yet. If you can get free pig food from a local factory or supermarket and have somewhere to keep pigs it might just be worth keeping a pig. To dip you toe in the water you could buy half a pig from a farmer and process it into sausages / salami / chorizo / chops / cured legs etc. That might put you off. Expect to pay £1 per kilogram for the pig. Some of this will be waste of course.
Compare this to 500 grams of supermarket cooking bacon for 81 pence and you might think keeping a couple of pigs is too much trouble.
Rabbits
I have not kept these myself. Apparently they breed like rabbits. My friend kept his in a cage and just tips the grass clippings from work over them. When there seemed to be too many he eat one. During the winter they need to be fed on straw. So he reduced the number of rabbits in autumn.
If all this sounds like a good idea you should consider being a small holder. Get yourself at least an acre of land. I recommend Seymour in further reading.
All of which brings me to common land.