They need to first route check it via CFMU, iterate it if it is initially rejected, and then they need to stuff the route into some site that files the flight plan. It's no rocket science; anybody can drive CFMU with a script, and a private agreement (with an AIS unit) for filing the verified plan is all one needs.
I think the reason we don't get web-based flight plan filing from anybody remotely connected with the UK establishment is most likely 99% political. This facility has been talked about since I started flying 5-6 years ago; it's one of the most obvious things to do in aviation.
As for providing GA facilities, one problem is that UK pilots don't want to pay for anything. Among UK's VFR population, the market for services such as these is undoubtedly very thin.