Often yes under permitted development, but exceptions and size limits mean you should check before building.
Permitted development rights are a legal exemption from planning permission, and you must stay within the current size and height limits to rely on them.
Listed building consent is a separate legal requirement from planning permission, and works without it are a criminal offence.
Building regulations approval is a separate legal requirement from planning permission, and most extension work must comply with it.
The Party Wall Act requires you to serve notice on neighbours before certain work on or near a shared boundary.
Councils have legal powers to take enforcement action against unauthorised building work.
Scotland and Northern Ireland have their own planning and building control laws, separate from England and Wales.