Converting an existing residential cellar or basement into a living space is in most cases unlikely to require planning permission, as long as it is not a separate unit, the usage is not significantly changed and no alterations are made to the external appearance of the property.
Excavating to create a new basement which involves major works, a new separate unit of accommodation and/or alters the external appearance of the house, such as adding a light well, is likely to require planning permission.
If you live in a listed building you are likely to need consent for internal or external work.
In all circumstances you are advised to contact your local planning authority for guidance on local policy before starting any work.
Disclaimer - Wales
This is an introductory guide and is not a definitive source of legal information. This guidance relates to the planning regime for Wales. Policy in England may differ. If in doubt contact your Local Planning Authority.