Cobbler
It's a good question. For historical reasons, the use of SVFR in the UK is a bit odd. The UK has class A CTRs (and had the equivalent before ICAO alphabet soup caught on) where SVFR is the only option for visual flight regardless of weather conditions. To prevent PPLs with no instrument qualification from scud running through the London CTR in silly visibilities, a licence privilege restriction demands a 10 km minimum visibility for them. This was the same as the old VFR minimum vis in controlled airspace (5 nm) and so it used to facilitate access to what are now class A CTRs on about the same terms as others. Since then the VFR minima have changed.
If you have an IMC rating, the min vis drops to 3000 m. If you have an IR, there's no licence privilege minimum vis, but a minimum visibility at the airport is usually required for a SVFR clearance to be issued (typically 1500 m).
Incidentally, I think the purpose of SVFR is better stated as allowing a flight that is unwilling to comply with IFR to enter or leave controlled airspace. It's not necessarily aimed at increasing the flexibility of the basic PPL. In the US, although a basic PPL allows SVFR during the day, an IR is required at night.