How can I judge reputation of a publisher? Any rankings? Correct me if I'm wrong: identity of publishers affects quality of a publication. E.g., OUP and CUP feels like the most reputable and trustworthy in the UK, as Oxbridge are globally renowned.

But how can unknown publishers be judged, like those unconnected with any top universities?
There are no rankings of publishers I'm aware of (what criteria would you even use?); however, my experience is that academics also barely care about the prestige of the publisher. If there are any publishers at all whose names carry weight, it's CUP and OUP.

Just make sure not to publish with a predatory publisher and you should be set.