The 1851 has her birth as Bristol:
William J Marks 38 Cardiff, Glamorganshire
Harriet L Marks 36 Bristol,
William T Marks 13 Bristol,
Harriet L Marks 10 Bristol,
Alfred J Marks 8 Bristol,
Edwin Marks 6 Bristol,
John Marks 4 Bristol,
Jeremiah Marks 1 Bristol,
HO107/1947 / 212 pg 27
Though presuming this is her in 1861, it has her husband William as from Bristol, not Cardiff
William Marks 49 Bristol,
Harriet Marks 47
Alfred Marks 18
RG09/1712 / 97 pg 28
Modified to add: Harriet's maiden name is CLYNE on the GRO for the births of most of the children, just to give you another spelling.
