Prompt D meson and non-prompt J/ψ yields are studied as a function of the multiplicity of charged particles produced in inelastic proton-proton collisions at a centreof-mass energy of √ s = 7 TeV. The results are reported as a ratio between yields in a given multiplicity interval normalised to the multiplicity-integrated ones (relative yields). They are shown as a function of the multiplicity of charged particles normalised to the average value for inelastic collisions (relative charged-particle multiplicity). D0 , D+ and D∗+ mesons are measured in five pT intervals from 1 GeV/c to 20 GeV/c and for |y| < 0.5 via their hadronic decays. The D-meson relative yield is found to increase with increasing charged-particle multiplicity. For events with multiplicity six times higher than the average multiplicity of inelastic collisions, a yield enhancement of a factor about 15 relative to the multiplicity-integrated yield in inelastic collisions is observed. The yield enhancement is independent of transverse momentum within the uncertainties of the measurement. The D0 -meson relative yield is also measured as a function of the relative multiplicity at forward pseudo-rapidity. The non-prompt J/ψ, i.e. the B hadron, contribution to the inclusive J/ψ production is measured in the di-electron decay channel at central rapidity. It is evaluated for pT > 1.3 GeV/c and |y| < 0.9, and extrapolated to pT > 0. The fraction of non-prompt J/ψ in the inclusive J/ψ yields shows no dependence on the charged-particle multiplicity at central rapidity. Charm and beauty hadron relative yields exhibit a similar increase with increasing charged-particle multiplicity. The measurements are compared to PYTHIA 8, EPOS 3 and percolation calculations.