In areas where the local council has taken over control of parking matters (i.e. where you'll see council staff 'giving out tickets' rather than traffic wardens) it is a 'contravention' (not an 'offence') for a vehicle to be "parked with one or more wheels on or over a footpath or any part of a road other than a carriageway", leading to a 'Code 62' (higher level) penalty charge notice (PCN).
The powers of local councils to issue PCNs, and to enforce payment of the penalties, are derived from the Traffic Management Act 2004, which creates civil penalties for most parking contraventions, replacing the criminal offences which were defined under earlier Highways Acts.
Chris