"A calculatedly awkward design in plain, sheer concrete."
"The Buildings of England", Nikolaus Pevsner and Simon Bradley
Milton Court (completed in April 1965) was the first brave outpost of the Barbican enterprise. It is near the corner of Willoughby House and Speed House opposite Britannic Tower. In a sense it is still an outpost because its only connection to the Barbican Estate is a rickety footbridge from the far edge of Willoughby Highwalk.
In all the Barbican plans it is 'the Public Service Building' and it housed the fire brigade, a mortuary, the coroner’s court and a social services office. (It is slightly worrying that the first thing the City Corporation thought a community of 2,014 flats would need was a mortuary). The City Corporation also built two storeys of maisonettes on top to house all the staff who would be working on the new Barbican Estate. The building was completed in 1965 - whereupon it dawned on the Corporation that since they hadn’t built the Barbican yet, there were no staff to house in it. So they called it Milton Court and let the flats instead.
The fire brigade and social services have now moved out, the flat owners have been bought out, and clearly it is going to be replaced - but with what I do not know.