Hi
Not sure how your Hampshire/Lincolnshire/Nottinghamshire Drake family tie in with the 'London family' of John Drake esquire or as yet with London?
Thomas Carter Lane Drake's line
JOHN DRAKE
ELIZABETH LANE
Marriage: 17 JUL 1811 Saint Marys, Portsea, Hampshire
Widow and widower
THOMAS CARTER DRAKE
Christening: 04 JUL 1819 Quarrington, Lincoln
Father: JOHN DRAKE
Mother: ELIZABETH
possible second baptism or different Thomas - Sleaford is the birthplace given for Thomas Carter Lane Drake (butcher) on censuses
THOMAS DRAKE
Christening: 16 NOV 1821 New Sleaford, Lincoln
Father: JOHN DRAKE
Mother: ELIZABETH
sibling
MARY ANN DRAKE
Christening: 26 JAN 1817 Quarrington, Lincoln
Father: JOHN DRAKE
Mother: ELIZABETH
buried 17th December 1818 Quarrington infant
Meanwhile in London John Drake esquire married Maria in Bloomsbury and had two daughters baptised there
Known children
John Minshall Drake 1810 Cheriton Kent
(father of the 1851 census 'grandchildren' Captain in 46th Regiment)Caroline Drake 1816
Charlotte Augusta Drake 1818
William Henry Drake
(executor of father's will)William Henry Drake looks to be this man
'William Henry Drake born Coimbra, Portugal 1812- Died London 1882. Was Commissariat of the British Army and was stationed in Western Australia from 1830-1848 and in Hobart from 1848-1850. He married Louisa Purkis in Perth, Australia.' He secondly married Elizabeth Lucy ? a much younger wife who was born at the Cape of Good Hope and on his death left a will which indicated he had been knighted and was Sir William Henry Drake K.C.B.
http://trove.nla.gov.au/work/35932591?selectedversion=NBD10127167&c=collectionHis father John Drake was from Devon (1851 census) and was still married to his wife Maria who was from County Durham on the 1851 census.
I think you might have to unpick what you have inherited very carefully starting from what is known and proved, even if that means coming back into the C20th and then step by step going back each generation.
Regards
Valda