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?
The status of a danger area is what a Danger Area Activity Information Service will give you, which is not the same thing as a Flight Information Service.
Say you're flying around East Anglia, talking to nobody (it's the weekend so there's no LARS, and anyway it's a nice day so you don't need it). You want to know whether D207 is active because your passengers decide they'd like you to fly out over the Wash. Having checked the legend of your chart in advance you happen to know that the DAAIS for D207 is provided by London Information (some are, some aren't, see other thread). You call:
"London Information, G-ABCD, request danger area activity information for delta 207"
"G-ABCD, delta 207 is cold"
"G-ABCD thank you and good day"
Then you go back to talking to nobody (possibly with London Information tuned in and the volume turned down, if you like). No flight information service established.