SVFR is always conducted under an ATC clearance, and in the UK MATS Part 1 requires that
Controllers shall not issue a Special VFR clearance to any aircraft, other than helicopters, for departure from an aerodrome within a control zone when the official meteorological report indicates that the visibility is 1800 m or less or the cloud ceiling is less than 600 feet.
The proposal for the Standard European Rules of the Air would require a ceiling of at least 600 ft and a ground vis of not less than 1500 m (800 m for helicopters).
Note this is ceiling (50% cover or more) not base.