Jane Bourne's birth certificate gives her parents as John and Mary Bourne, formerly Vaughan. Jane was with her mother in the 1851 and 1861 Censuses and with both her parents in the 1841 Census.
In fact there are 10 children listed in the 1841 Census. Mary appears to have been 18 years younger than John, but in the 1861 census her age is given as 7 years older than would be expected from the two previous censuses.

The fact that Jane's parents were John Bourne and Mary Vaughan seems fairly certain.

Mary was apparently born in about 1801 or 1794 in Birmingham.