There certainly are men by the name of NEESAM at Brompton who could be the father of Martha Bradley and her siblings.

This article in the York Herald of 11 May 1876 shows a likely candidate:
Assault - Jane NEESAM was summoned for assaulting Mary Ann BROWN at Brompton on the 2nd inst. Plaintiff went to see defendant's husband about some money he owed her for the support of her three illegitimate children, of whom he had been adjudged the father, when defendant threw a pailful of water over her. Fined 6d. and 8s costs.

If I remember right I was earlier looking at a widower called NEESAM living with a widow called BROWN in later censuses.

Familysearch has baptism of a William John BRADLEY 14 Jan 1874 at Northallerton, Mother Mary BRADLEY, batch C04057-1.
I don't see a baptism for a Martha BRADLEY.

Bryan