These two figures adorn the clock of St Dunstan’s in the West, Fleet Street. They are meant to represent the Giants that inhabited the land of Albion (Britain) and were discovered by Brutus of Troy.
This story is all down to Geoffrey of Monmouth who wrote a history of Britain around 1136, he’s the guy that wrote about King Arthur. Like most of his stories there is a grain of truth here and there. The names Gog and Magog appear in Christian, Hebrew and Islamic teaching. Gog is a person and Magog is the land he inhabits. Geoffrey of Monmouth combines these two into one persona, that of Gogmagog the Giant of Albion.
This myth along with the religious references gave birth to the figures who ring the bell of the clock. The London legend is that the Roman Emperor Dioclitian had thirty-three rather wicked and wanton daughters, so he found thirty-three husbands to try and curb their excesses. They were not happy about this and under the leadership of the eldest sister, Alba, they murdered their husbands. As a punishment they were cast adrift in a boat eventually landing on a windswept island, which they named “Albion” after Alba. Here they hooked up with a tribe of demons and gave birth to a race of giants, whose descendants included Gog and Magog. They are the guardians of the City of London and every year their effigies are carried through the streets during the Lord Mayors Show.
I’ve never found out which one is which, it’s not as easy as identifying Ant & Dec.