John Webster was a Londoner, the son of a prosperous coachmaker, also John Webster, and his wife Elizabeth (née Coates). The family business was based in Cow Lane a few hundred yards north-west of the old city wall in the West Smithfield district where the Websters were based throughout John's life. In fact, we don't know precisely when he was born or died — the Great Fire of London in 1666 destroyed many of the capital's official records, including those which would have contained details of his baptism and burial — but his parents were married in November 1577 and he probably came into the world within a year or two. He had a younger brother, Edward (c. 1590-1644), and probably more than one sister.
Wiggins, Martin. "John Webster". The Literary Encyclopedia. First published 20 November 2001
[https://www.litencyc.com/php/speople.php?rec=true&UID=4643, accessed 18 February 2019.]