Hi all

The birth found by Elizabeth seems to match this christening:
John Lake, 20 Sep 1842, St Botolph Bishopsgate, London
Father John, mother Elizabeth
This looks like the John/Elizabeth family in 1851:
1851HO107/1542 636 8
St Matthew Bethnal Green, Middlesex
5 New StreetJohn Lake, head, 34, Cordwainer, b. Hampstead
Elizabeth, wife, 33, Shoe Binder, b. Bethnal Green
Elizabeth, dau, 14, Shoe Binder, b. Bethnal Green
Mary Ann, dau, 11, Shoe Binder, b. Bishopsgate
John, son, 7, Home, b. St Lukes
Robert, son, 4, b. Bethnal Green
Jane, dau, 6 mo, b. do.
Bridget Hamilton, lodger, wid, 27, Shoe Binder, b. St James Westminter
(Makes one wonder whether the first boy died)