We perform the first calculation of form factors in the semileptonic decays B → D1(2420)ℓνℓ and B → {D}_1^{prime } (2430)ℓνℓ using QCD light-cone sum rules (LCSRs) with B-meson distribution amplitudes. In this calculation the c-quark mass is finite. Analytical expressions for two-particle contributions up to twist four are obtained. To disentangle the D1 and {D}_1^{prime } contributions in the LCSRs, we suggest a novel approach that introduces a combination of two interpolating currents for these charmed mesons. To fix all the parameters in the LCSRs, we use the two-point QCD sum rules for the decay constants of D1 and {D}_1^{prime } mesons augmented by a single experimental input, that is the B → D1(2420)ℓνℓ decay width. We provide numerical results for all B → D1 and B → {D}_1^{prime } form factors. As a byproduct, we also obtain the D1- and {D}_1^{prime } -meson decay constants and predict the lepton-flavour universality ratios R(D1) and R( {D}_1^{prime } ).

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