Well I have finally cured the problem. I removed all the programs that looked as though they might dial of there own accord to no joy.
I then found a piece on another PC forum mentioning an option to stop a PC on a network with internet connection sharing from dialling a connection when one is not present. The option is on the PC that actually owns the internet connection and once the option was selected the problem was cured.
The only downside is that if you want internet access on PC2 then PC1 has to be instructed to connect but in my case this is not a problem.
I can't remember where I found the option but I can find it again if anybody is desparate to know.