Aha....XDA to the rescue...
And finally, a new fault, bug or issue of my own... Wi-fi...
Alas, it seems there's a major issue with the wi-fi in my SGS3... I switch my phone on, and it fires up, and sees and connects to my home wi-fi... But if I try and USE the net or data connection, it's a dog's dinner... If I run a Mobile Speed-test, I get a terrible ping, an average download speed of 0.02 Mbps, and then it times out three quarters through with a connection error.
It has done this since I got it Wednesday. However, I can confirm it is the PHONE, not my home wi-fi, as my Router is very new and mega-top end, and my three SGS2's are working absolutely fine on it. Moreover, if I pull the Notification Tray down on my SGS3, then disable Wi-fi, then pull back down, then re-enable, and then run the speed test again, I get great pings, 22Mbps Downlaod, and 5Mbs uplaod speed (my Home Internet is 100Mb).
So clearly pointing to an issue with the phone. It does this on both 2.4GHz, and 5Ghz, as my router is full dual channel, independent. Looks like either a faulted phone (hope not), or a fault in current Kernel of the software, which would be better, if a fix was forthcoming.
This bit is really bothering me though - a brand new device, and it's the only device in my home that has issues with connectivity and web.
Argh...