“Common Land” is actually a bit of a misnomer. All land in the UK is owned by somebody – be it an individual or an organisation.
The term “common land” simply denotes land which is owned by someone, but over which other people have rights protected in law, be it local, regional or national. A good example is the right to pasture cattle on common land.
Unless there are public rights of way across said land then you may not have a right to cross it, as local by-laws may prevent access. That said, little is likely to come of it if you do go exploring and somebody objects.