For APC-esque fit, Uniqlo skinny cut was similar, just marginally looser throughout. The newer ones are meant to be similar and just have shittier fabric composition, but I have yet to try. Shouldn't be more than £40 to try though, less if you're near enough to try in-store.
Are those HL jeans the last season's coated ones? Or original HL from when he still did menswear?