  We suppose that the observed neutrino masses can be parametrised by a lepton
number violating dimension-five operator, and calculate the mixing of double
insertions of this operator into lepton flavour changing dimension-six
operators of the standard model effective theory. This allows to predict the
log-enhanced, but $m_\nu^2$-suppressed lepton flavour violation that is generic
to high-scale Majorana neutrino mass models. We also consider the Two Higgs
Doublet Model, where the second Higgs allows the construction of three
additional dimension-five operators, and evaluate the corresponding anomalous
dimensions. The sensitivity of current searches for lepton flavour violation to
these additional Wilson coefficients is then examined.
