Socket to consumer unit

I am installing one socket in my garage for a tumble dryer and connecting it to a separate fuse in my consumer unit. Do I need to loop it ie two lives,neutral and earth or can I just use the one cable like a spur

It just needs to be a radial, one feed cable. What rating fuse are you using? Why not just connect it to the ring main in your house? Is the socket RCD protected? It could reasonably be used to supply outdoor appliances, so it should be, unless you fit a 15A round pin socket and an FCU, or connect the dryer into the mains (via an FCU) directly.

Connect it as a radial.
Before energising, test continuity of CPC, measure value of R1 + R2 and enter this on your Electrical Installation Certificate. Test insulation resistance between all conductors.
Energise circuit and measure Earth Loop Impedance and trip time of RCD as adding additional sockets places a responsibility on you to provide RCD protection to sockets that can reasonably used for portable equipment outside equipotential zone.

Use a B16 MCB Breaker, feeding a length of 2.5.mm cable (check for Voltage Drop and Earth Loop Impedance etc), and onto a 13amp socket for the Appliance.
As said before the essential RCD must be tested for tripping time etc.