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Very much a long shot, but could it actually be Costock, which is in Nottinghamshire but only about 2-miles from the Leicestershire border?

The Baptist registers for Sheepshead/Shepshed, Leics have the following:

Elizabeth King d/o Jonadab King and his wife Ann was born Costock in the County of Nottingham on 5 Feb 1785

Other children were Ann (1787) and Sarah (1790).

Jonadab King of Costock married Ann Oram otp at Shepshed on 7 Jul 1783. He died 25 Jan 1838 at Costock but was buried in the Baptist Chapel Burial Ground, Shepshed.

His will is available to order from the Borthwick Institute in York.

Nothing listed for either of them, sorry.

Sorry I'm not sure what you're asking?

One is the 1871 census you already posted the Ancestry link for (attendant at Essex Lunatic Asylum), and the other is the daughter of George & Caroline.

I would say so, although finding the correct death may be hard as its not exactly a common name and she could be anywhere 

This makes no sense at the moment, but since James was in Great Baddow in 1871 & 1881 as a servant to John Crabb it seems too much of a coincidence not to be connected.

There is an article in the Chelmsford Chronicle 31 Dec 1880 about the suicide at Great Baddow of David Spackman, coachman to Mrs Crabb (who I think is the wife of Richard H Crabb).  A witness at the inquest was "Harriet Harris, wife of James Harris of Great Baddow"

The only James Harris I can see in Great Baddow in 1881 is 'your' James, and the only Harriet Harris is on the same census page, just a few properties away:

Harriet Harris 54 b Wyke, Dorset
Harriet Hansford 22 Niece b Great Power(?) Street, City, Middlesex
Beatrice Young 8 Visitor b Woolwich, Kent

By 1891 James & Harriet are back in London, at 73 Pulford Street, St George Hanover Square
James Harris 63 born Brentford, Middx, Coffee Tavern Keeper
Harriet 63 wife b Wyke, Dorset
Harriet 28 Niece b City of London
also three boarders and a servant

(Edited to correct spelling!)