Rights of Way

The law on public access is quite complicated, but Cycling UK has a useful summary and explanation (for England and Wales) 

Note that a footpath in the countryside is not the same as a footway/pavement alongside a road. Cycling on a footpath is classed as a trespass against the landowner, which is normally a civil offence rather than a criminal one, unless specific byelaws apply. This means that the landowner can sue the trespasser for damages in the civil courts, but the police are not involved and there’s no criminal record for the offender.

Cycling on a footway or pavement is illegal under Section 72 of the 1835 Highway Act, which makes it an offence to ride on “any footpath or causeway by the side of any road.” Although the original act predates the bicycle, it is referred to in Rule 64 of the current Highway Code. The same section also prohibits the use of e-scooters on pavements (see Department of Transport Guidance on Powered transporters).