In message , Basil Jet
writes

Back to our Angel of the Underground, does anyone know the purpose of the
octagonal building bearing LU signs at the junction of Goswell Road and City
Road, and when it was built?

I'm pretty sure it's the surface exit from the emergency stairs at Angel
station, constructed in 1992 when the station was rebuilt with separate
platforms instead of the former narrow island platform. It's close to
the old station entrance, which was almost opposite.
--
Paul Terry