Steinmeier and his wife Elke Budenbender were then joined by UK Culture Secretary Lisa Nandy at the Victoria and Albert Museum's East Storehouse, where the museum's archive has been put on display - including some of pop star David Bowie's costumes and instruments.
Bowie had strong associations with Berlin, having lived and worked in the city in the 1970s.
They later joined the Lady Mayor of the City of London, Dame Susan Langley, for an evening banquet at the Guildhall, with the Princess Royal also in attendance.
Earlier in the day, the pair had left Windsor Castle for London - though not before being shown Queen Victoria's winter sleigh, designed by her German-born husband Prince Albert in 1842, and attending a charity reception.
They visited Westminster Abbey and laid a wreath at the Grave of the Unknown Warrior, which symbolises those who died serving in World War One, particularly those who were not buried.
The final day of his state visit on Friday will see Steinmeier visit the ruins of Coventry Cathedral, bombed by the German air force during World War Two, in a symbolic gesture of reconciliation.
This mirrors a visit to Hamburg during the UK state visit to Germany, when King Charles laid a wreath remembering the civilian casualties of wartime Allied bombing raids.
He will also receive an honorary degree from Oxford University, on a trip in which he will learn about medical research at the university.