Gertrude, an interesting comment
No. You can establish two-way communication for other purposes. In particular you can call London Information for all sorts of things, such as requesting the status of a danger area, without either asking for or receiving flight information service.
I would ask what is 'the status of a danger area' if it isn't flight information?
Maybe the issue here is that in the UK because we offer ATC outside CAS and there are so many different services available we went for this concept of the pilot negotiating a service with the controller - i.e., pilot asks for X, controller agrees to provide it. We don't do this inside CAS - typically an aircraft gets airborne, pilot checks in with DEPARTURE/APPROACH and gets told 'identified, radar control'.
And then there's the business of what services you get when in communication with ATC. In the example above it's fairly clear, radar control = air traffic control. The pilot is also getting FIS and ALR despite the fact there's been no mention of them - hence my assertion that the moment you are in communication with an ATC unit you get FIS/ALR because they are the basic levels of ATS that are just always provided by any ATS. When a pilot on airways asks ATC for the wx somewhere downroute what he/she is asking for and getting is FIS (not ATC). If an aircraft force lands ATC will tell the emergency services where it landed - the pilot is then getting an ALR.
Your example of a practice PAN is especially interesting. Although you may be calling London Centre (and I'm not sure where D AND D is done from these days - not that it matters for this discussion), I think 121.500 is a special case and dedicated to ALR and so the issue of requesting or getting a FIS is not relevant.