OK, I'm giving up on this.
There's no single site online that gives positive results with this.
I now have full internet 'connectivity' at a disappointing speed of typically less than 10 Mbit/sec.
The effective range of the AP is about 8 metres in G-mode and less than 5 metres in N-mode.
I've discarded the RTL8188CUS based dongle and bought one that identifies itself as being RaLink RT3070.
That one has an effective range of at least 20 metres.
My advice to every reader of this:
Don't buy a dongle with a RTL8188CUS chipset. According to most sites there are a few good brands (for example Edimax), but most other brands of these dongles are cheap Chinese imitations that are completely worthless.
You have been warned...