  We report theoretical results for magnetic field induced $2p^53s^3P_{0,2} -
2p^6^1S_0$ E1 transitions in Ne-like ions with zero nuclear spin (I=0) between
Mg III and Zn XXI as well as in Ne I. We demonstrate that it is important to
include both ``perturber'' states $2p^53s^1P_1$ and $2p^53s^3P_1$ in order to
produce reliable transition rates. Furthermore, we investigate the trends of
the rates along the isoelectronic sequence of the $2p^53s^3P_{0,2} - 2p^6^1S_0$
transitions and their competition with the $2p^53s^3P_0 - 2p^53s^3P_1$ M1 and
the $2p^53s^3P_2 - 2p^6^1S_0$ M2 decays. For the $2p^53s^3P_0$ state the
magnetic field induced transition becomes the dominant decay channel for the
light elements even in a relatively weak magnetic field, and it will therefore
prove useful in diagnostics of the strength of magnetic fields in different
plasmas. The influence of an external magnetic field on the lifetime of the
$2p^53s^3P_2$ state is much smaller but still observable for the ions near the
neutral end of the sequence. As a special case, the magnetic field effect on
the lifetimes of $2p^53s^3P_{0,2}$ states of neutral $^{20}$Ne is discussed. It
is found that the lifetimes are drastically reduced by a magnetic field, which
may be an underlying reason for the discrepancies in the lifetime of the
$2p^53s^3P_2$ state between experiment (14.73(14) s) and theory (17.63 s).
