I have had a look in the bin stores and there are brown bins in the left bin stores (looking at them) of both 100 and 101 Rope Street. These have the same code as all other bin stores, so you do have access. I do not know why the council has not put them in 1 South Sea or at 7 RQ. This may be deliberate as perhaps the lorry does not collect down South Sea Street.
If you contact the council they should be best placed to help, as this initiative has nothing to do with the buildings manager or their agent.