MOT handbrake failure

My Sportline just failed its MOT on the Off-side back brake. The handbrake is failing to work and giving a read of 12% or less efficiency. The garage have quoted me £70 -£100 to replace the cable. I heard tho that it's quite common for them to seize up and be quite easily unseized with a bit of manual persuasion/ adjustment. Problem is I live in central London, have no access to a ramp and currently very few tools. Has anyone had a similar problem, and if I do get the garage to take a look, do you think this is a fair price?

Just wanted to add the nearside is working perfectly!

handbrake cable = 15 notes
2 hour labour = 50-70 notes (more likely an hours labour but they dont know what else they will find.)