I would think that this is down to the insurance policy that you took out. Check the small print.

Most people go for the cheaper options which have more exclusions, if so you may not be covered.

I suspect that the flights between Manila and the UK would be covered as they are on the same ticket - but not the Cebu Pacific flight.

The insurance company would argue that you didn't give yourself enough time at Manila, you should be there 2-3 hours prior to your flight departs so I suspect they would say that you should have allowed a greater time window and caught an earlier flight to Manila.

Fingers crossed for you.