Simon,
As I understand it. If you miss the flight because of a public transport failure (that would I guess include a taxi etc,) you are covered, but I did ask a long while ago and was told it did not cover my son breaking down, being delayed etc., when he was taking me to the airport in his car.
Define public transport....... a mode of transport available to the public like a taxi, train, bus or plane maybe
The only way to be sure (but not for missed check-ins as I described) when more than one leg is involved is to book all the flights in the same booking. That way the airlines are responsible.
Which is what I said about booking the whole journey through a travel agent
Also as I said, one company I know do cover passengers flying from Spain to UK for transfers, providing there is at least 3 hours gap. But I did say, that was something which was included as a 'special' as I had pointed out the problem experienced by people living in Spain who often make two bookings, one to the UK and one to the final destination.
When taking out insurance one needs to read the conditions very carefully, but I know it's the last thing we do as we just think 'we must be covered.'
Totally agree........always read the small print
Off the main thread but I think relevant.
Years ago I used to let my apartment in Spain for holidays. I discovered by chance that if my apartment had become unusable, say by fire, and I could not find alternative accommodation, then the flight/holiday insurance did not cover that. The insurers all said it would be my responsibility to cover all the costs, including the flights and compensation, as I had contracted to provide the service. I tried very hard to find insurance to cover me but could not.

Surely you would look at you household insurance to cover any expenses if something happened to your apartment.