If you can stop the specific problematic plane taking off then keeping the system running is fine, but once you have a flight in the air it's a different game.
It's not totally unreasonable to say "we have an aircraft en route to enter UK airspace and we don't know when or where - stop planning more flights until we know where that plane is".
If you really can't handle the flight plan, I imagine a reasonable solution would be to somehow force the incoming plane to redirect and land before reaching the UK, until you can work out where it's actually going, but that's definitely something that needs to wait for manual intervention anyway.