Working with a pion mass $m_pi approx 150$ MeV, we study $pipi$ and $Kpi$ scattering using two flavours of non-perturbatively improved Wilson fermions at a lattice spacing $aapprox 0.071$ fm. Employing two lattice volumes with linear spatial extents of $N_s=48$ and $N_s=64$ points and moving frames, we extract the phase shifts for p-wave $pipi$ and $Kpi$ scattering near the $rho$ and $K^*$ resonances.Comparing our results to those of previous lattice studies, that used pion masses ranging from about 200 MeV up to 470 MeV, we find that the coupling $g_{rhopipi}$ appears to be remarkably constant as a function of $m_{pi}$.