If a tree on my property is blown over in strong winds and falls onto a neighbour's property causing damage, am I in any way liable for the damage? Or is it an act of God for which the neighbour can claim under his own house insurance? Thanks in advance for any info.
I think you will find it's your tree, so your problem and liability. There's a clause in your buildings insurance that will provide you with cover for this risk - as part of the standard T&Cs.
You can only be successfully sued for something if the other person suffered loss or damage either through your deliberate actions or through your negligence.
Without proof (based upon the 'balance of probabilities') of 'intent' or 'negligence', any civil action against you would be doomed to failure.