As you are not the owner of the bike, it will surely be “Cyclescheme” that would need to make the warranty claim.
OTOH, if this is through Edinburgh Bike Co-ops own scheme then your employer owns the bike and it would be their responsibility to chase up any warranty – although there may (should) be a procedure in place.
22. What happens if my bicycle has a warranty problem during the hire agreement period?
When you choose your bicycle equipment, Edinburgh Bicycle Cooperative will advise you of the warranty period, as they vary with each bicycle.
If you experience problems within the duration of the warranty period, take your bicycle back to the Edinburgh Bicycle Cooperative who will liaise with the supplier on your behalf.