Most of the time its just an insurance company trying to ring more money out of you.
If you have insurance from any EU country you are covered for the legal minimum insurance that is required in the EU country you are visiting. That may only be third party injury insurance.
Most companies will renew/issue Green Cards over the phone if you use your credit card to pay for it, go for 60 days, then renew for another 60 and so on. You can just write onto the green card the extended dates, the original will be sent to your UK address so you can produce it if necessary at a later date.
Be sparing with information that you give the insurer, dont say "I'm in Gibralter and need to extend my green card". "I'm just about to head off on another trip and need to get a green card" is more appropriate.