hello Dave - this is a bit puzzling as although I can find mentions of the streets being named after the Vaughton family no one seems to explain who Robert Vaughton was.
I have found - using various web sites - that Robert Darwin Voughton/Vaughton (b.1795 - d.1851) married Mary Ann Dymoke (b.1809 -d.1881)
They had a son Robert Dymoke Vaughton.
Robert Dymoke Vaughton was a Lieutenant colonel he married Emily Boultbee (b.1826)
Emily Boultbee was the daughter of Joseph Moore Boultbee (b.1791-d.1860 - buried Balsall, Warwickshire) and Lady Elizabeth Margaret Townshend (b.1791-d.1868) who married at Baddesley Clinton in 1815
Lady Elizabeth Margaret Townshend was the daughter of of George Townshend, 2nd Marquess Townshend (b.1753 -d.1811) and Charlotte Ellerker (d.1802)
One of their other daughters, Lady Harriet Anne Townshend (d.1845) - Married Edward Ferrers in 1813 - he lived at Baddesley Clinton (which possibly explains why her younger sister Lady Elizabeth Margaret got married there). Baddesley Clinton is the large moated manor house owned by the National Trust.
According to google maps the Streets are still there in B12 there is also a Darwin street.
Robert Dymoke Vaughton obviously married into a wealthy family but maybe the Vaughtons were wealthy too - without more information on the Vaughtons it is difficult to say who once owned the land where the streets are.
An old map may help solve whose estate the land was on.
Polly