In response to the main thread, Stein Financial specialise in arranging insurance products for pilots. Russ Stein, who owns the operation, is also a pilot and aircraft owner so well worth a chat as he understands things from the flyers perspective.
Dave,
With regard to your query, under EU law it is the responsibility of the aircraft owner or operator to arrange at least specified minimum levels of cover for their liability for death or injury to third parties arising out of the use of their aircraft. There are also minimum requirements in terms of passenger liability (and cargo and baggage for commercial carriage).
If you are not the aircraft owner then the best bet is to check with the owner before you fly to see what level of cover they have and that you are included as a pilot.
Cheers
Bob