A VFR flight plan is delivered only to those explicitly addressed, plus a copy goes into a "national security database" of some sort to which various agencies have access, and from where it gets fished out if you disappear.
If it is addressed to an airport where you are not landing, they will bin it, so it does not assist with getting a CAS transit.
Since in the UK Class G you can change between VFR and IFR purely inside your head, with no radio contact, there is very little point in filing VFR flight plans unless you desire the rescue angle to be addressed (no pun intended).
IFR flight plans are processed via a totally different system, involving a computer in Brussels (with a backup system in Paris, I believe). The route, once validated etc, is acknowledged with an ACK message and then X minutes (usually about 600) before EOBT the flight plan is transmitted to the various endpoint and enroute IFR units. It's a very smooth system, but it is unsuitable for UK Class G low level hacking under IFR because, as I say above, nobody except the endpoints will be interested in it, so you may as well file VFR.
The above notes apply to Europe only and in some cases to UK only. In much of Europe, not the UK though, any flight plan is distributed immediately to the whole country so if you call up some ATC unit in France they can see what you are on about very quickly. The UK system is fairly tightly partitioned between the IFR/CAS sectors, and the dross flying below that, with ATC funding arrangements and other politics keeping things where they are. Countries with a nationalised ATC system tend to have things working better.
Some notes are
here and
here.