The NA62 experiment at CERN collected a large sample of charged kaon decays into final states with multiple charged particles in 2017-2018. Results from searches for lepton flavour and number violating decays in $K^+$ and $\pi^0$ to final states containing a lepton pair, based on this data set, are presented, reaching sensitivities of $\mathcal{O}(10^{−11}−10^{−10})$.