The UK does fund SMEs, that's the Innovate UK program. It's a good pot for domestic money and relatively easy to get (or used to be, you'd see the same companies at every conference). It has money for solo industry and industry/university projects. It's under the same umbrella (UKRI) that also funds academic research (STFC, EPSRC, AHRC, etc).

For some comprison with Switzerland where I currently live, and who also has a rocky relationship with the EU - we have InnoSuisse which every startup seems to get money from, and SNSF which is the massively oversubscribed science funding agency.