AFAIK in the UK they are addressed manually, by looking up addresses in a big book of airports like a phone directory.
If you use the excellent homebriefing.com flight plan filing service (Euro 36/year) they have a computer system for this, which contains that "book" in a database.
There are a lot of quirks in this process. For example, if the destination is LEAX (a sleepy place somewhere near Malaga, unmanned much of the time) then the FP should be addressed to LEMG (Malaga) and this sort of stuff is often done wrong, and is a big reason for VFR flight plans going missing, and having to be filed again when you are sitting all ready to go at the field of departure and the OAT is +35C
The other thing which is dodgy is using the DOF/ facility. In the manual system, I have been told by one ATCO, the ATCO sticks any FP that has a DOF/ on it on a clip on the wall and files it on the specified date. This often fails if e.g. he is off work on that day. Homebriefing.com get around this by injecting the FP into the system only on the specified day of flight.