I believe the compensation part only kicks in if it’s the airline’s fault.

You may be right. As a direct result of the NATS issue perhaps not, but any second order issues once that is resolve you might be within scope.

Almost certainly not. The legislation says: "An operating air carrier shall not be obliged to pay compensation [...], if it can prove that the cancellation is caused by extraordinary circumstances which could not have been avoided even if all reasonable measures had been taken."

That gets them off the hook for even second order effects. No harm throwing in a claim though, there's no penalty for having a claim turned down.

NATS had failed once, so it failing again doesn't seem extraordinary to me.

It is however extraordinary, and there don't seem to be any reasonable measures a carrier could take to work around it.

Fair point.

I think the qualifying rules may have changed since then.

The legislation is on the link below, it might be worth a once-over with your chat bot of choice to understand out if your circumstances are covered:

https://www.legislation.gov.uk/eur/2004/261/contents