ABSTRACT The Survey for Distant Solar Twins aims to find stars very similar to the Sun at distances of 1–$4\, {\rm kpc}$, several times more distant than any currently known solar twins and analogues. The goal is to identify the best stars with which to test whether the fine-structure constant, α, varies with dark matter density in our Galaxy. Here, we use epic, our line-by-line differential technique, to measure the stellar parameters – effective temperature Teff, surface gravity log g, and metallicity [Fe/H] – from moderate-resolution (R ≲ 32 000) spectra of 877 solar twin and analogue candidates (547 at 1–$4\, {\rm kpc}$) observed with the High Efficiency and Resolution Multi-Element Spectrograph (HERMES) on the Anglo-Australian Telescope. These are consistent with expectations for Teff and log g from photometry, and for [Fe/H] from the Besançon stellar population model. epic provides small enough uncertainties ($\sim 90\, {\rm K}$, $0.08\, {\rm dex}$, and $0.05\, {\rm dex}$, respectively), even at the low signal-to-noise ratios available (${\rm S/N}\gtrsim$ 25 per pixel), to identify 299 new solar analogues ($\ge 90~{{\ \rm per\ cent}}$ confidence) and 20 solar twins (≥50 per cent confidence), 206 and 12 of which are at 1–$4\, {\rm kpc}$. By extending epic to measure line broadening and lithium abundance from HERMES spectra, and with ages derived from isochrone fitting with our stellar parameters, we identify 174 solar analogues at 1–$4\, {\rm kpc}$ that are relatively inactive, slowly rotating, and with no evidence of spectroscopic binarity. These are the preferred targets for follow-up spectroscopy to measure α.