This is basically a "struggle" between the UK (where the service is privatised and under pressure to terminate all services not making money - unless mandated by ICAO) and the rest of the world (where this stuff is not generally privatised).
Every airport tower must provide a flight plan filing service, under ICAO. How they do it is their business (within the UK, the man in the tower will generally type it into AFPEx, or one the older AFTN terminals) but a pilot must be able to just hand in a handwritten ICAO flight plan and have it processed.
It doesn't have to be done for free, however.