Presumably you need to know where upcoming flights are going to be in the future (based on the plan), before they hit radar etc.
In this regard UK ATC can choose to do anything they like with a plane when it comes under their control - if they don't consider the flight plan to be valid or safe they can just instruct the plane to hold/divert/land etc.
I'm not sure the NATS system that failed has the ability to reject a given flight plan back upstream.
I have no idea what percent of the volume into the UK comes from outside radar control; if they asked a flight to divert, that may open multiple other cans of worms.
Any ATC system has to be resilient enough to handle a diversion on account of things like bad weather, mechanical failure or a medical emergency. In fact, I would think the diversion of one aircraft would be less of a problem than those caused by bad weather, and certainly less than the problem caused by this failure. Furthermore, I would guess that the mitigation would be just to manually direct the flight according to the accepted flight plan, as it was a completely valid one.
One of the many problems here is that they could not identify the problem-triggering flight plan for hours, and only with the assistance of the vendor's engineers. Another is that the system had immediately foreclosed on that option anyway, by shutting down.