© 2021, The Author(s).Decays of B mesons with leptons in the final state offer an interesting laboratory to search for possible effects of physics from beyond the Standard Model. In view of puzzling patterns in experimental data, the violation of lepton flavour universality is an interesting option. We present a strategy, utilising ratios of leptonic and semileptonic B decays, where the elements | Vub| and | Vcb| of the Cabibbo–Kobayashi–Maskawa (CKM) matrix cancel, to constrain the short-distance coefficients of (pseudo)-scalar, vector and tensor operator contributions. The individual branching ratios allow us then to extract also the CKM matrix elements, even in the presence of new-physics contributions. Bounds on unmeasured leptonic and semileptonic decays offer important additional constraints. In our comprehensive analysis, we give also predictions for decays which have not yet been measured in a variety of scenarios.