How best to add sockets to a fused spur?
UK wiring standards.

Your builder is half right and half wrong.

(a) Is the circuit a ring circuit or a radial circuit? Standard circuits are:


ring circuit, wired in 2.5mm cable with a 30A fuse or 32A circuit
breaker 
radial circuit, wired in 2.5mm cable with a 20A fuse or circuit breaker 
radial circuit, wired in 4mm cable with a 30A fuse or 32A circuit breaker


If the circuit is a ring circuit then an unfused spur can supply a maximum of one single or one double socket. A fused spur, as you propose, can supply an unlimited number of sockets with a maximum load of 13A.

Your building is proposing extending the ring. To do this correctly a second cable would have to be run back to the point where the spur is taken from the ring, and the ring broken with each side connecting to one side of the new wiring. Connecting to another part of the ring randomly to form a 'figure 8' circuit is not permitted. 

If the circuit is a radial circuit then it can be extended with an unfused spur-off-a-spur as the cable is sized to carry the whole load of the circuit at any point. The radial must be extended in the same size cable as the existing circuit.