Talktalk connection dropping after heavy rain?

I have used TalkTalk for my first experience of broadband. Very satisfied so far.....
But … I get Internet 'connection' problems for several days often, by coincidence, after periods of heavy rain. The router light for the internet doesn't come on and the DSL one flashes. Router is zyxel 600 series.

Phone works fine. Filter/splitter thingy ok. Wireless router has been checked and is ok. Master socket is ok – have used the little test socket to check too.

Other than just waiting till it chooses to work again you can sometimes get it to work for a while by using the phone. It's almost as if the electrical activity of the phone call helps it to connect. (Similar to when car won't start because battery is flattish then someone comes along turns the key and it fires!)

Could there be damp in a connection 'their' side? I have to pay for engineers call out if they can't find anything wrong on their side, as I just know I'm going to struggle to explain this to them.