How do new faculty members in the UK start their career without startup grants?
Research grants for new academic staff are offered competitively by the various research councils, depending on your subject area.

You can learn about the various research councils and what grants they operate through the web site for Research Councils UK.

For Computer Science you should be eligible for an EPSRC New Investigator Award, however the competition is fierce, so you should be sure to seek the advice and support of the research office of your University who can assist you in writing a successful grant proposal.

Some Universities, as noted, do offer their own support for new academics, but irrespective of funding available locally there is national funding, and also perhaps one might also look at European Funding for new researchers whilsts the window of opportunity remains open.

For an ambitious and promising researcher the position is not necessarily as pessimistic as you might feel.