Greetings from mizzly Cornwall !
If you do ever find 10yr old Robert Bartholomew Beckwith in the 1861 census, please do let me know ! Ditto his mother Ann nee Bartholomew. Some of Robert's siblings have been recorded with surname Bartholomew but I have tried that too as well as all mis-spellings I can think of.
Robert's father Joseph Beckwith b1776 died in Dec 1860 at the family's "Clarendon" coffee house at 77 Shoe Lane, London EC (not listed in 1861 census as mentioned in other posts).
I too was fooled by the "East London" bit in the FreeBMD register entry until I found that it was the name applied to the eastern part of central London, in Robert's case the parish of St Brides. Mind you, he did later venture into 'real' East London - Poplar no less.
There's a bit more on Robert in para 8.54 of
http://www.luxsoft.demon.co.uk/beckwith/tree-1%20notes.htmlWhat's also curious is that although Joseph & Ann ran the coffee house in Shoe Lane in 1851, they had moved to the Walworth / Camberwell area by 1854 and, according to an 1860 trade directory, ran a Coffee House in what is now John Ruskin St.
Ann is still in the coffee house business south of the river in 1871 (166 Bermondsey St) ...so why is Joseph's death recorded in Shoe Lane ?
Happy hunting !