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no deeper than 10cm
This is gonna make things tough, so I think the sound bar is the right call. For eg these small front ported active speakers I've got saved from some recommendation somewhere are still 18cm.
https://www.amazon.co.uk/gp/product/B06XGC7NTX/ref=ox_sc_saved_title_2?smid=A2V8YV6FAC397E&psc=1
If you are just after something better than shit you could mount a sound bar underneath the desk.
Another option is getting some cheap but not shit cube speakers (this sort of thing but idk about these in particular) and pair with a sub.
Having little monitor style speakers plus a sub is very unaudiophile, but a very practical way of getting better sound - especially for the volumes I assume you're going to be listening at. I had a Creative set up like that, and it worked very well for my office desk.
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I have one of these on my desk which I got years ago as a birthday present.. Sound is OK and fairly neutral compared with most portable speakers..
The sound on my monitor is shit so I'd like something better. With a widescreen monitor and a fairly narrow desk there isn't much space so I'm thinking of some form of soundbar under the monitor. Are there any small ones that don't have rubbish sound? Preferably no wider than 50cm and no deeper than 10cm. Ideally under £100 but could stretch to more.
Or willing to listen to any other bright ideas people have.