The surrogate ratio method has been tested for ($p,d$) and ($p,t$) reactions on uranium nuclei. ${}^{236}$U and ${}^{238}$U targets were bombarded with 28-MeV protons and the light ion recoils and fission fragments were detected using the Silicon Telescope Array for Reaction Studies detector array at the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory. The ($p$,$df$) reaction channels on ${}^{236}$U and ${}^{238}$U targets were used as a surrogate to determine the $\ensuremath{\sigma}$[${}^{236}$U($n$,$f$)]/$\ensuremath{\sigma}$[${}^{234}$U($n$,$f$)] cross-section ratio. The ($p$,$tf$) reaction channels were also measured with the same targets as a surrogate for the $\ensuremath{\sigma}$[${}^{235}$U($n$,$f$)]/$\ensuremath{\sigma}$[(${}^{233}$U($n$,$f$)] ratio. For the ($p$,$df$) and ($p$,$tf$) surrogate measurements, there is good agreement with accepted ($n$,$f$) values over equivalent neutron energy ranges of ${E}_{n}=0$--7 MeV and ${E}_{n}=0$--5.5 MeV, respectively. An internal surrogate ratio method comparing the ($p,d$) and ($p$,$t$) reaction channels on a single target is also discussed. The $\ensuremath{\sigma}$[${}^{234}$U($n$,$f$)]/$\ensuremath{\sigma}$[${}^{233}$U($n$,$f$)] and $\ensuremath{\sigma}$[${}^{236}$U($n$,$f$)]/$\ensuremath{\sigma}$[${}^{235}$U($n$,$f$)] cross-section ratios are extracted using this method for the ${}^{236}$U and ${}^{238}$U targets, respectively. The resulting fission cross-section ratios show relatively good agreement with accepted values up to ${E}_{n}\ensuremath{\sim}5$ MeV.