I saw the Green Mace at Firepower Museum in Woolwich this afternoon. Its in "Building 41" housing a number of prototypes that never got off the ground.
I believe many of the items were previously at other museums (the other RA museum - The Rotunda) that were closed and have ended up at Woolwich as it is the only area big enough to house them. (building 41 is one of the old depots from the Munitions days)
They aren't spending any money on the building as it is just a storage facility, and the museum itself is closing in 2016. All the military and munitions buildings in Woolwich will soon be apartment blocks.
The large items such as Green Mace will be taken to Larkhill (RA headquarters in Wiltshire) between now and the 2016 closure date so if you want to see it get down asap.
Building 41 is closed off (as someone previously mentioned) but if you ask a member of staff there should always be someone who will open it up and let you walk round, or if you are lucky a Volunteer can give you a tour. Many of the Volunteers themselves are ex-Royal Artillery so can give you an interesting and informative tour. The Museum is open Tuesday to Saturday (closed Sunday & Monday) and I would recommend going on Saturday as there are more Volunteers and less MOD staff who can be a bit sniffy about going in this area.