GBP10 seems to me to be about the minimum you can expect to be charged, for a job that literally takes 2 minutes. Gear tuning where there are problems that cannot be solved by the barrel adjuster (fiddling with the adjuster is a genuine 2 minute job) is going to be more.
You’re not paying for the time it takes to adjust something, you’re paying for the knowing what to adjust.
This. + knowing how!
However common sense should’ve told you that going to a big flashy bike shop you were going to get a big flashy bill. Did it have a bell on the door so they can keep the scum out?