Energy levels, wavelengths and radiative decay rates have been calculated for states within the 4p k (k = 1-5) and 4d k (k = 1-9) ground configurations in highly charged tungsten ions. Magnetic dipole (M1) and electric quadrupole (E2) transition probabilities have been obtained using the fully relativistic multiconfiguration Dirac-Fock (MCDF) approach including the correlations within the n = 4 complex, some n = 4 → n = 5 single excitations and quantum electrodynamics effects. The validity of the method is assessed through limited comparison with experimental and theoretical data previously published as well as with new relativistic Hartree-Fock calculations. The excellent agreement observed between our new MCDF A-values and those obtained using different theoretical approaches together with a detailed analysis of configuration interaction effects does not confirm the very recent GRASP2K calculations of Jonauskas et al (2012 At. Data Nucl. Data Tables 98 19) for M1 lines within the 4d k configurations, the latter results remaining in large disagreement with all other methods in many cases.