The
type of car park might be an important consideration here:
Section 170 of the Road Traffic Act 1988 applies "on a road or other public place":
https://www.legislation.gov.uk/ukpga/1988/52/section/170
A "public place", for the purposes of the Act, includes areas to which the public generally have access (such as supermarket car parks and NCP car parks) but excludes areas which are only for use by restricted categories of people (such as a car park provided by a company only for use by its staff and visitors to the site):
http://www.counsel.direct/news/2015/11/18/what-is-a-public-place-in-the-context-of-the-road-traffic-act
Note that the requirement to report an accident to the police only cuts in when no notification of the relevant details has been provided to the driver of the other vehicle. Simply leaving a note on the windscreen of the unoccupied vehicle, bearing the required information, is likely to be all that's needed in most cases.