Short answers, pulled from the story.
Southwark is a district of Central London on the south bank of the Thames and is the oldest part of South London. Its significance traces back to around 43 AD, when Roman engineers chose the site for the first bridge across the Thames in the area. That bridge determined the location of Londinium, the Roman city that grew into modern London.
The name Southwark derives from the Old English words suth (south) and weorc (work or fortification), meaning "southern defensive work." Its earliest recorded form, Suthriganaweorc, appears in the 10th-century Anglo-Saxon document known as the Burghal Hidage and means "fort of the men of Surrey." By 1086, the Domesday Book recorded the name as Sudweca.
John Harvard attended the parish free school of St Saviour's in Southwark and later studied at the University of Cambridge. He emigrated to the Massachusetts Bay Colony and left his library and a substantial donation to a new college in Cambridge, Massachusetts, which was named Harvard University in his honor. Harvard University alumni later funded a memorial chapel in Southwark Cathedral, his family's parish church.
Shakespeare worked at The Rose, Southwark's first playhouse, opened by Philip Henslowe in 1587. In 1599, he was a shareholder in the Globe Theatre, erected on the Bankside within the Liberty of the Clink. The Globe burned down in 1613, was rebuilt in 1614, and was closed by the Puritans in 1642.
The nursery rhyme may originate in a battle fought at Southwark's London Bridge during the 1014-1016 war for control of London. According to Snorri Sturluson's saga, Olaf II Haraldsson tied ropes to the bridge's supporting posts and pulled the structure into the river, helping King Ethelred the Unready retake the city from the Danes.
Notable people born in Southwark include Sir Keir Starmer, born in 1962, who serves as Prime Minister of the United Kingdom; the actor Michael Caine, born in 1933; the singer Siouxsie Sioux, born Susan Janet Ballion in 1957; and historian and television presenter Lucy Worsley, born in 1973.