The Museum of London is sort of in the Barbican estate, if you extend the boundary to include the podium and high-walks round the corner of Aldersgate Street into London Wall. I am not sure who designed or built it.
It doesn’t look as if it was built as part of the estate itself. Instead of being encased in concrete, its surface seems to be made entirely of white bathroom tiles. But on the other hand, the tiles look so similar to the original Barbican bathroom design that perhaps this was a precursor of Lord Rogers’ Lloyd’s Building, showing the inside (in this case Barbican bathrooms) on the outside. The London Museum even has something like a soap dispenser or electric hand dryer sticking out the side.
The Museum has always seemed a rather undistinguished building. It looked squeezed into a gap, much the way you would fill a hole with mastic. But in recent years it has had a facelift, with a new entrance, a cafe, and external seating areas.
Like the Tardis, it seems a lot bigger inside than outside. It is easy to get disoriented, but I think it must extend into that corn silo thing which forms the roundabout at the corner of London Wall and Aldersgate Street.
It seems to be a very worthy effort to create a museum. It ekes out some leftovers of the Roman era with lots of dressed up wax models and visualisations. Some hugely ornate carriages used in The Lord Mayor’s processions are also parked there.
I believe the Museum authorities want to move to a larger site, and there is talk of converting the entire corner into a new concert hall.