There is an alternative
practical point of view on all this which is: don't call up any ATC unit unless they can offer you something you need.
In Class G (uncontrolled airspace) you can fly non-radio. If you are qualified to fly in IMC then you can do that non-radio too. And you have nice peace and quiet in the cockpit!
Personally, I don't call up anybody unless they can offer a
radar service.
And London Information can't (even if the man had a radar screen in front of him he would not be allowed, due to ATC job demarcation, to use it to help you).
I find that most experienced pilots do exactly this - fly with a listening watch only, tuned in so they can always make a mayday call should they need to. The people who call up London Info tend to be PPL students (who have been trained to call up every Tom Dick and Harry and pass on their inside leg measurement), or people after some specific services (e.g. opening flight plans, checking danger area status, weather for some remote airport...)
Of course one cannot tell this to the RT examiner
Radar Information is a
UK only concept. Outside the UK you get just FIS (which is a basic ICAO requirement) but some countries are more pragmatic and if the controller has a radar screen (which most of them seem to have, especially France) then he lets it be known (with perhaps the informal words "radar contact") that he can see where you are, may pass you details of conflicting traffic, and because he can see where you are he doesn't have to waste his and your time asking you for position reports with estimates to XYZ; something which London Info will do and which can keep you quite busy enough! Unless you have the route programmed in a GPS and can see the ETA to each waypoint, of course
As regards which unit can offer you an FIS, this isn't so complicated in practice. The FIS frequencies (together with the name of the unit) are marked on all ICAO compliant VFR charts. Very often, probably nearly always, this station name is not related to any airport. It is just somebody sitting in some room hundreds of miles away.
One can get an FIS from airports but the more usual thing is to call up the regional FIS shown on the map.
In the UK, a lot of people call up an airport (rather than London Info) for FIS, in the hope that they get better information on traffic flying in the vicinity of that airport, but that is IMHO a waste of time unless the said airport can offer a radar service. Otherwise you get "five aircraft known in the area" which is as much use as a chocolate teapot
Unfortunately, I don't think one can make use of the European slant when doing a UK RT exam. Which is no doubt why one gets so many Brits venturing into France and asking for a Radar Information Service...