I don't have a reference for the 2011 pay-per-file which I can quote, as this was put to me with some vehemnce by an ex-NATS employee, who I don't care to name. This does fit with my perception of the world, however, so I'll be pleasantly surprised if this doesn't happen...
I agree it may happen because NATS accountants see GA as a waste of their money.
But if it does happen, it will merely play into the hands of any State owned tom dick or harry outfit outside the UK who has an AFTN terminal and wants to start up a flight plan filing service. It takes all of a few days' work to knock up a website with a flight plan form on it, Paypal/Worldpay prepay accounts, and off you go.
AFAIK a number of years ago the airlines stopped using UK facilities for flight plan filing and have been doing it via flight support services which inject the FPs into the AFTN via terminals in the USA. This resulted in the Heathrow FBU filing almost entirely just GA VFR flight plans; thousands per month so it is no wonder they were eventually closed.
Outside the UK, we don't have the privatised ATC / airport structures with crazy artificial accounting separation and there are lots and lots of establishments who can offer a commercial service - like homebriefing.com which is an offshoot of Vienna ATC.