  The aim of this work is to use gamma-ray burst supernovae (GRB-SNe) as
cosmological probes to measure the Hubble constant, $H_0$, in the local
Universe. In the context of the Expanding Photosphere Method (EPM), I use
empirically derived dilution factors of a sample of nearby SNe Ic, which were
derived in Paper I of a two-paper series, as a proxy for the dilution factors
of GRB-SNe. It is seen that the dilution factors as a function of temperature
in $VI$ display the least amount of scatter, relative to $BVI$ and $BV$. A
power-law function is fit to the former, and is used to derive model dilution
factors which are then used to derive EPM distances to GRB-SNe 1998bw and
2003lw: $36.7\pm9.6$ and $372.2\pm137.1$ Mpc, respectively. In linear Hubble
diagrams in filters $BVR$, I determine the offset of the Hubble ridge line, and
armed with the peak absolute magnitudes in these filters for the two
aforementioned GRB-SNe, I find a (weighted average) Hubble constant of
$\bar{H_{0,\rm w}} = 61.9\pm12.3$ km s$^{-1}$ Mpc$^{-1}$ for GRB-SNe located at
redshifts $z\le0.1$. The 20\% error is consistent with the value of $H_0$
calculated by Planck and SNe Ia within 1$\sigma$. I tested the fitting method
on five nearby SNe Ic, and found that their EPM distances varied by 18-50\%,
with smaller errors found for those SNe which had more numerous usable
observations. For SN 2002ap, its EPM distance was overestimated by 18\%, and if
the distance to SN 1998bw was similarly over-estimated by the same amount, the
resultant value of the Hubble constant is $H_0 = 72$ km s$^{-1}$ Mpc$^{-1}$,
which perfectly matches that obtained using SNe Ia. [abridged]
