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We don't know. This happened during Shakespeare's "Lost Years" about which we have no information.
Shakespeare did his work in London to keep William Shakespeare alive.
In London, England
There is little known of William Shakespeare's marriage, or even Shakespeare himself. What we do know is that after Shakespeare retired from theatrical life in London, he moved back in with his wife in Stratford as if nothing had happened, an event which argues that they were happily married even if often apart.
The only place we know that Shakespeare worked was in London.
He moved to London in the 1580s
William Shakespeare lived from 1564 until 1616. The Great Fire of London was in 1666 so the answer to your question is 'no'.
It was in London, England that William Shakespeare established himself as an actor and playwright. It was also here that he began writing sonnets and poetry while the theaters were closed due to the plague.
During his entire career, Shakespeare was based in London, England.
William Shakespeare arrived in London in 1588. However this date is disputed because the period of 1585 to 1592 not much was known about Shakespeare's whereabouts.
Shakespeare's children were Susanna, Judith, and Hamnet whether he was in London, Stratford, or anywhere else.
Charles Dickens William Shakespeare