Ever since I've had my iPhone 5S, I've had problems with the wifi on my 120 MB Virgin SuperHub. Quite often the phone fails to connect to sites, or the wifi connection drops out. I've even tried re-installing iOS to see if it was a corrupt operating system (as the "Genius" at the Genius Bar suggested).
It turns out that going into the wireless settings of the Virgin SuperHub and changing the "Wireless Band" parameter from 2.4GHz to 5GHz, with a channel setting of "Auto Compatability" fixed my problem.
I'm placing this on my blog so it can be found by anyone with similar issues.