…the word 'road' has been widely interpreted by the courts to be any place to which the public has access.
I’m not so sure. Not recently, anyway.
There is a clear distinction in the wording between that in s87 (the requirement for a licence) which mentions only “a road” and that in s144 (the requirement for TP insurance) which mentions “a road or other public place”.
Interestingly, the “other public place” extension was not added to s144 until 2000. If the legislators had thought it necessary to add it to s87 as well, they could have done so but didn't. This seems to me to indicate that they believed there should be a distinction between the two.
There may have been some interpretation of “a road” (for s144 offences) needed prior to that.