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We perform the first calculation of form factors in the semileptonic decays$B\!\to\! D_1(2420)\ell\nu_\ell$ and $B \to D_1^\prime (2430)\ell \nu_\ell$using QCD light-cone sum rules (LCSRs) with $B$-meson distribution amplitudes.In this calculation the $c$-quark mass is finite. Analytical expressions fortwo-particle contributions up to twist four are obtained. To disentangle the$D_1$ and $D_1^\prime$ contributions in the LCSRs, we suggest a novel approachthat introduces a combination of two interpolating currents for these charmedmesons. To fix all the parameters in the LCSRs, we use the two-point QCD sumrules for the decay constants of $D_1$ and $D_1^\prime$ mesons augmented by asingle experimental input, that is the $B \to D_1(2420)\ell\nu_\ell$ decaywidth. We provide numerical results for all $B\to D_1$ and $B\to D_1^\prime$form factors. As a byproduct, we also obtain the $D_1$- and $D_1'$-meson decayconstants and predict the lepton-flavour universality ratios $R(D_1)$ and$R(D_1')$.

$B\to D_1(2420)$ and $B\to D_1'(2430)$ form factors from QCD light-cone sum rules