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The measured $\overline{B}\ensuremath{\rightarrow}{D}^{(*)}l\overline{\ensuremath{\nu}}$ decay rates for light leptons ($l=e$, $\ensuremath{\mu}$) constrain all $\overline{B}\ensuremath{\rightarrow}{D}^{(*)}$ semileptonic form factors, by including both the leading and $\mathcal{O}({\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}/{m}_{c,b})$ subleading Isgur-Wise functions in the heavy quark effective theory. We perform a novel combined fit to the $\overline{B}\ensuremath{\rightarrow}{D}^{(*)}l\overline{\ensuremath{\nu}}$ decay distributions to predict the $\overline{B}\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\tau}\overline{\ensuremath{\nu}}$ rates and determine the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cb}|$. Most theoretical and experimental papers have neglected uncertainties in the predictions for form factor ratios at order ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}/{m}_{c,b}$, which we include. We also calculate $\mathcal{O}({\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}/{m}_{c,b})$ and $\mathcal{O}({\ensuremath{\alpha}}_{s})$ contributions to semileptonic $\overline{B}\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ decays for all possible $b\ensuremath{\rightarrow}c$ currents. This result has not been available for the tensor current form factors, and for two of those, which are $\mathcal{O}({\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}/{m}_{c,b})$, the corrections are of the same order as approximations used in the literature. These results allow us to determine with improved precision how new physics may affect the $\overline{B}\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\tau}\overline{\ensuremath{\nu}}$ rates. Our predictions can be systematically improved with more data; they need not rely on lattice QCD results, although these can be incorporated.