That's because a VFR flight plan cannot (in modern Europe) be refused
Could you develop a bit on that? I haven't had one refused so far, but my understanding is that it can, for a host of things, such as PPR not requested/obtained when necessary, airfield being closed or unable to accommodate your flight, wrong FPL information, etc., etc.
I will certainly miss this service.
Having filed many a verbal flight plan on the mobile on the way to the airport

That's that mean that you cannot just phone up
any airport in the UK and ask them to file in a flight plan for you?