As you wrote, the general details on his family are that he had 3 brothers , Thomas, William and John. John being a sweep, the others on the railway. Sussex Railway employees called Jones are quite likely to be too numerous to track down, but its worth a try.
Another record however states his two sisters (Catherine and Anne) were both married, so both should appear on the Sussex Marriage Index, hopefully wedded to someone with a surname that is in less frequent use. Perhaps you could find the sisters on the SMI and then locate them on the 1851 census to deduce their and possibly George's birth place from that? Finding them may also reveal who their parents were.
A Catherine Jones who married a Joseph Baly in Brighton 1827, might be worth following up. The couple appeared in Clerkenwell in 1841.
SFHG also have a baptism in Withyham for a John Jones from a travelling family.
John JONES, Baptism Date 25-Dec 1818, Father John, mother Jane
Father's Occupation travelling chimney sweeper Abode Hailsham
Notes note ""see April. 9. 1817""
Parish Withyham, East Sussex
Roy G