@PRofessorSlocombe
this might interest you, since you're interested in precision:
"2. What is a highway?
There is no statutory definition of a highway, only a common law one.
Halsbury’s Laws states:
A highway is a way over which there exists a public right of
passage, that is to say a right for all Her Majesty's subjects at all
seasons of the year freely and at their will to pass and repass
without let or hindrance. A highway may be dedicated subject to
certain restrictions or obstructions; and it may be limited to a
recognised class of traffic, that is it need not be a way for vehicles,
as, if they are open to the public generally, footpaths, bridleways
and driftways are highways. It is, however, an essential
characteristic of a highway that every member of the public
should have a right to use it for the appropriate class of traffic;
there can be no dedication to a limited section of the public, such
as the inhabitants of a parish.
13
A “highway maintainable at the public expense” is defined in section 36
of the Highways Act 1980, as amended. It states that a highway:
… shall not … become a highway which for the purposes of this
Act is a highway maintainable at the public expense unless
either—
(a) it was a highway before 31st August 1835; or
(b) it became a highway after that date and has at some
time been maintainable by the inhabitants at large of any
area or a highway maintainable at the public expense;
and a highway shall not by virtue of that subsection cease to be a
highway maintainable at the public expense if it is a highway
which under any rule of law would become a highway
maintainable by reason of enclosure but is prevented from
becoming such a highway by section 51…
It further requires every local highway authority (unitary and county
councils) “cause to be made, and shall keep corrected up to date, a list
of the streets within their area which are highways maintainable at the
public expense”.
Some private or unadopted roads are highways, but not all, and the
position is not always easy to determine. In his 2013 book Private
Roads: The Legal Framework (5th ed.), Andrew Barsby explains the
difficulties of dealing with definitions in this area:
The courts have generally taken the view that the public has
access to a road is members of the public actually use it and the
use is tolerated, even if there is no actual right to use the road […]
a private road which was actually used by the public would be
within the definition of a “road” … even if it was not (or not yet)
a highway…
This definition of “road” enables legislation to apply to all
highways, including private roads which are highways, and to
some other private roads which are in fact used by the public.14"
TL:DR - some private roads are also highways, some are not. What you can do with your private road depends on whether or not it is also a highway. Also, public rights of way are not limited to "non-cars" - vehicular access may be restricted to certain classes of vehicle but that could include cars.