Moving line (unless you go out of your way to tell both Openreach and your ISP), will leave you disconnected at the new address.

In reply to:

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Anyhow, I'm assuming it does as I can see that there is connectivity but, no web pages will load or e-mails download via outlook express.

I'm puzzled, my mum phoned plus net (her IP) and they said that the router wasn't connected. Surely it is, as you get details of your connection speed in the bottom right hand corner when turning the computer on??

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For any number of reasons, I shall not bore you with, your folks new line is connected via broadband port in the exchange that is not theirs/allocated to them, hence the sync, but no PPP.
The firstly need to find out from Plusnet, wether or not their account with them is still active, and to what address PN believe they are supplying it....if the answers are yes, and the new address, they need to get PN to get OR to deal with this........
if not, then it's time to order a new service.

Good luck.

Cheers!