Not clear to me whether these right granted by a private contract e.g. covenant in a deed or by virtue of public planning policy: local land charge/Baulast) in favour of the Local Authority or Highway Authority etc.

Anyway, the right to build below land would be virtually redundant in the UK, as most structures need to be built on underground foundations.

Even an underground garage would be covered by the Eng. Common law rule of the right to excavate and dig right down into the subsoil and to the 'centre of the earth'.