We report the discovery of an esdL3 subdwarf, ULAS J020858.62+020657.0, and a usdL4.5 subdwarf, ULAS J230711.01+014447.1. They were identified as L subdwarfs by optical spectra obtained with the Gran Telescopio Canarias, and followed up by optical-to-near-infrared spectroscopy with the Very Large Telescope. We also obtained an optical-to-near-infrared spectrum of a previously known L subdwarf, ULAS J135058.85+081506.8, and reclassified it as a usdL3 subdwarf. These three objects all have typical halo kinematics. They have Teff around 2050-2250 K, -1.8 ≤ [Fe/H] ≤ -1.5, and mass around 0.0822-0.0833 M⊙, according to model spectral fitting and evolutionary models. These sources are likely halo transitional brown dwarfs with unsteady hydrogen fusion, as their masses are just below the hydrogen-burning minimum mass, which is ˜ 0.0845 M⊙ at [Fe/H] = -1.6 and ˜ 0.0855 M⊙ at [Fe/H] = -1.8. Including these, there are now nine objects in the `halo brown dwarf transition zone', which is a `substellar subdwarf gap' that spans a wide temperature range within a narrow mass range of the substellar population.