If I understand the article:

• a flight plan is a series of waypoints.

• Waypoints are represented using identifiers that are known to not be globally unique.

• an algorithm attempts to extract the portion of the flight in the UK airspace failed due to one of the non-unique waypoints in a flight plan

• the failure caused the primary system to halt

• the backup system takes over, processes the same flight plan and fails the same way, halting as well

• UK air traffic control can no longer accept/process flight plans, preventing flights from happening

• it took a while to resolve the system error, and longer to resolve the impacted people