This depends where you want to paddle. Most lakes in the UK are in private ownership, and you need the landowners permission.

If you're paddling a managed waterway (eg navigable river or canal) then you will almost certainly need a licence, normally from the Environment Agency or the Canal and River Trust.  but membership of British Canoeing gives you most of the licences you need to paddle on any licensed waterway.

Paddling on the sea or on estuaries does not require a licence, unless it is a harbour.  MOst harbour authorities require a licence or must give permission. Some, such as the authority managing the thames Tideway through London do not give a licence unless you've had specific safety training.

Find out more about access, licences, and British Canoeing membership