Lots of people offer this service, from large companies to small. There are also online guides and kits available from the web to do it yourself. I would say for the cost get it done at a reputable small shop. Whilst you are at it change the battery too. Usually a big discount for two jobs and a battery costs only £10 max.
FYI I have bought all the kits to do front/back/battery on an old iPhone4 I want as a backup. Haven’t sat down to do the job yet but I am seeing it as a hobby project and it’s an old phone anyway so don’t need it, so messing it up isn’t an issue.
EDIT: BTW you didn’t say front or back glass, it does make a difference as front has integrated touch sensor (I think). Also if you buy online look for feedback as some glass isn’t glass it’s cheap plastic especially for the back (which messes up camera lens)
@wysiwg is the man to ask