It is possible, but you have to think mostly of things like visas & work permits, you can't always just go into a country & work, because of laws & regulations.
You could get an open round the world air ticket for around £1000.
But I think your best bet is to do things little by little. Pick one country, research it well & go there. Then come home & work/save some more money for your next country.
You can travel cheaply - stay in hostels (which are basic but i'm a single girl & have stayed in a few hostels & would definitely do it again/recommend it!!) but I would say it's better to save some money up. I mean you want to make the most of your experience, if you have no money you might miss out on things you know?
Good luck.