Thankfully there have not been any more uninvited nasties on my reader list - well not for today at least. Thank you so much for your help - Tom in particular.
If anything like this happens to you (really hope that it doesn't) - but here's what I've done.
1. First of all, I contacted Google (did that yesterday) - on their help page. You describe the problem and then the next stage is to highlight the bits that are causing you grief. Submit the lot to them.
2. I changed my Google Account password. If you type in 'Google Account' - they walk you through the necessary. I also added a double layer of protection by allowing Google to send a verification code to my phone.
3. Dug out the ethernet cable like Tom said and changed my Home Hub password.
So hopefully things will be OK