Paul - parking on a pavement always causes an unnecessary obstruction - the Offence is committed; whether the Police prosecute is a different matter.
There are defences including:
(1) Being directed by a Police Officer
(2) Parking signs displayed stating you can
amongst others.
There is very rarely specific laws in this country 'naming the offence' but there are other laws that cover it.
e.g. Swearing in public isn't a specific offence but it is covered by the Public Order Act.
From your link to the RAC:
Rule 242 is where it gets a little less clear, stating: "You MUST NOT leave your vehicle or trailer in a dangerous position or where it causes any unnecessary obstruction of the road."
This is a must not, again, meaning if your car is reported or seen by a police officer and judged to be either in a dangerous position or causing an unnecessary obstruction of the road, you could receive a Fixed Penalty Notice.