I don't know where you have read that, but it is not an accurate representation of the regulations.
An unfused spur is a single cable connected to a ring circuit at an accessory or a junction box, this is permitted to feed one, and only one, point. That point can be a single socket twin socket (but not two singles), fused connection unit (FCU) or switched fused connection unit (SFCU)
A fused spur is connected to a ring circuit via an FCU or SFCU, this can supply as many points as you like as long as the cables are suitably sized etc etc.
What you have described is an unused spur feeding two points, the first point is an SFCU and the second point is the socket you wish to change. This is not permitted by the regulations.
Have you confirmed that the circuit is in fact a ring circuit? What is the rating of the circuit breaker which feed it?