I have Elizabeth in my line. I have found that there are a number of John Streek's about, so it really depends if you can connect all of the children say through a common church or place.
It is not unknown to have two children born at different times baptized close together. It was sometimes done when a child was not expected to survive.
John's wife Ann, as far as I can make out from FreeBMD died Q2 1843 Easthampstead Berkshire ref 6-111.
John died Q4 1852? Easthampstead ref 2c 250. Same source.
I cannot find John and Ann on the 1841 census which would be a help. I looked at Easthampstead's two registration districts but they were very poor images, but I do not think that I missed them so they must have been elsewhere.
John was born Heckfield Hants c1777 baptized same 14/12/1777
of John Streek & Barbarah?
Is Ann's name only Ann Wardsworth as I have seen her referred to as Jane Wadsworth and also Ann Maria Wardsworth. Wadsworth is a much more likely name for the area (reference the brewery) and Googling does not produce much at all.