Hi Ester,
With respect, your approach may be wrong. In simple terms, your home insurance covers your property - your neighbour should claim on their insurance. You seem to be assuming that the public liability section of your policy should kick-in and your insurers should automatically pay the bill. It doesn't work like that.
As in most things in Spain there are some curious practices, so you may be successful, but I doubt it. Your neighbour should claim off their policy and not involve you or your insurers.
I don't know the full details, but as a general legal principle you are unlikely to be held liable for the incident outlined either in UK or Spain. So from Groupama's point of view why should they pay for something for which you are not liable ? Clearly they have misled you and their communication skills are lacking, but that's just the Spanish way.