  By use of the \textsc{grasp2018} package we perform Multiconfiguration
Dirac-Hartree-Fock (MCDHF) calculations with configuration interaction (CI) for
the $^{1}S_{0}$ and $^{3}P_{0,1}^o$ levels in neutral cadmium and mercury. By
supplying the resultant atomic state functions to the \textsc{ris4} program, we
evaluate the mass and field shift parameters for the $^{1}S_{0}-\,^{3}P_{0}^o$
(clock) and $^{1}S_{0}-\,^{3}P_{1}^o$ (intercombination) lines. We make revised
estimates of the nuclear charge parameters $\lambda^{A,A'}$ and differences in
mean-square charge radii $\delta\langle r^2\rangle^{A,A'}$ for both elements
and point out a discrepancy with tabulated data for Cd. In constructing a King
plot with the Hg lines we examine the second-order hyperfine interaction for
the $^{3}P_{0,1}^o$ levels. Isotope shifts for the clock transition have been
estimated from which we predict the unknown clock line frequencies in the
bosonic Hg isotopes and all the naturally occurring isotopes of Cd.
