May not be a son Peter that died in 1843 after all....There is a parish entry for a Peter Caird, father Peter, a baker, residing at 12 Malbro' Street, Chelsea who married an Ann Lane on 5 Jan 1845 at St Mary's Battersea.
So, so far we have possible siblings for Mary, a William and Peter but I am struggling on the census for 1841

There is this possibility on IGI for a marriage:
PETER CAIRD and MARY CAIRD Marriage: 21 AUG 1821 Saint James, Westminster