We study the soft electric dipole ($E1$) response of deformed halo nuclei ${}^{31}\mathrm{Ne}$ and ${}^{37}\mathrm{Mg}$ using a deformed Woods-Saxon potential, with the potential depth adjusted to reproduce empirical separation energy of the last neutron orbit, i.e., 150 keV for ${}^{31}\mathrm{Ne}$ and 220 keV for ${}^{37}\mathrm{Mg}$. The configuration dependence of the $E1$ strength near the neutron threshold is pointed out. The halo configurations $\left[321\right]3/2$ at ${\beta }_2=0.5$ and $\left[330\right]1/2$ at ${\beta }_2=0.24$ in ${}^{31}\mathrm{Ne}$ contain large amplitudes of halo $p$-shell orbits, which significantly enhance the threshold strength by several times compared to the non-halo configuration $\left[202\right]5/2$ at ${\beta }_2=0.32$. In ${}^{37}\mathrm{Mg}$, the last neutron configuration is assigned as $\left[321\right]1/2$ at a large deformation of ${\beta }_2=0.46$, which involves a halo $p$-shell configuration that significantly enhances the soft dipole strength. This enhancement is about 60% larger than that of the $\left[321\right]3/2$ configuration in ${}^{31}\mathrm{Ne}$ because of large $p$-shell probability in ${}^{37}\mathrm{Mg}$. Experimental confirmation of the soft dipole strength is highly desired to determine the deformation and the configuration of the last neutron orbits both in ${}^{31}\mathrm{Ne}$ and ${}^{37}\mathrm{Mg}$.

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• Collective levels
• Electromagnetic transitions
• Nuclear charge distribution
• Nuclear structure & decays
• Nucleon distribution
• 20 ≤ A ≤ 38