One little thing to be careful of.....the 10km viz is a restriction of a UK issued PPL, and not a restriction of SVFR itself. Therefore many pilots operating in the UK on a non UK issued PPL will not be subject to the 10km viz limitation.
This is also important when thinking of SVFR in other countries, where it is largely used to allow a flight that can't operate IFR (for whatever reason) to operate in meteorlogical conditions lower than VFR conditions.
GAW,
You are likely to use SVFR in two senaros,
1. You will to transit a class A zone. You can't accept IFR without an instrument rating, and there is no VFR in class A. Operating under SVFR allows you to still operate in the class A zone. SVFR is only available in a Zone, not any other type of airspace.
2. You wish to fly at night in a class D (or higher) zone. You can't accept IFR in class D or higher airspace, and you can't fly VFR at night. You can operate as a SVFR flight though
I hope that helps!