The cascading 3.21 MeV and 4.44 MeV electric quadrupole transitions have been observed from the Hoyle state at 7.65 MeV excitation energy in $^{12}$C, excited by the $^{12}$C(p,p$^{prime}$) reaction at 10.7 MeV proton energy. From the proton-$gamma$-$gamma$ triple coincidence data, a value of ${Gamma_{rm rad}}/{Gamma}=6.2(6) times 10^{-4}$ was obtained for the radiative branching ratio. Using our results, together with ${Gamma_{pi}^{E0}}/{Gamma}$ from Eriksen et al., Phys. Rev. C 102, 024320 and the currently adopted $Gamma_{pi}(E0)$ values, the radiative width of the Hoyle state is determined as $Gamma_{rm rad}=5.1(6) times 10^{-3}$ eV. This value is about 34% higher than the currently adopted value and will impact on models of stellar evolution and nucleosynthesis.
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