Hi
It depends what sort of records you want to search. If you visit The National Archives then searching records there is free. The National Archives has a vast amount of records, a small amount of which are accessible on the internet. To view any of the records, not just the indexes does cost.
Have you any reason to believe Robert's father ever came to London?
1851 census HO107 1526 folio 16
Duke Street St Bartholomew the Great City of London
Robert Sandford 25 Head Married Norfolk
Sarah Sandford 19 Wife Married London
On the 1871 census Robert states his birthplace as Saxham Suffolk (confirmed by the 1891 census in Southchurch Essex) his age as 46, and his occupation as a sewing machine maker.
There are two places called Saxham in Suffolk - Great or Little Saxham. Great Saxham has coverage for the period you are interested in on the IGI, Little Saxham doesn't.
There is no death registration for a Simon Sandford in the civil registration starting 1st July 1837.
There is this Prerogative Court of Canterbury will (at The National Archives) for a Simon Sandford in Suffolk but not a brewer. He might have a connection or he might not.
Will of Simon Sandford, Farmer of East Bergholt, Suffolk
Date 04 June 1832
Catalogue reference PROB 11/1801
http://www.nationalarchives.gov.uk/documentsonline/power-search.asp?searchType=powersearch8th January 1832 St Mary East Bergholt
Simon Samford? aged 85
Regards
Valda