Hi Fran,
Are you a member of NZSG?
They are holding seven Certificates for David (including possibly his baptism in 1816 in Kimbolton, Hun, England) and death in 1891.
Martha is also listed on some of them and Martha Mary.
There is also a school record admission for a Martha Mumford aged 4yrs in 1880 but no corresponding birth at BDM.
Further enquiries to Canterbury Branch NZSG.
BDM show no Mumford births in NZ prior to 1865 and those between 1865 and 1874 show no parents names, and those after 1874 have no David/Martha as parents

John B