Hey! I went to university for Game Art and I now work in the games industry. I completed an internship year 2022-23 that was part of a government backed scheme that required me to be finishing the 2nd year of university. So, in my one-person-experience, my choice to go to uni directly impacted my ability to get into industry.
I would say if you can get an apprenticeship/internship - sure, that's a really great option. But they are highly, highly competitive across the country and you will be competing with people who have probably already got a degree, or may not be eligible due to schemes like the one I did.
It also massively depends on what part of game development you want to get into. Artists are developers, coders are developers, designers are developers.... what is it you want to specialise in? Or are you interested in lots of areas of game development and want to indie dev/ work in a small team?
Generally coders/software engineers have the best odds of getting opportunities like degree apprenticeships etc. If you are more art-leaning you'll be looking at very few opportunities. You will need a very established 3D portfolio with lots of development breakdowns etc.
There are other options outside of "traditional" university, there's lots of online course options these days that certainly can match up to games education you'd get at uni. Obviously they would generally require you to front the cost instead of student loans, though, so it will depend if you are in a position to do that.
I can't speak to HNC/HND's - I don't know too much about them.
Happy to try and answer any other Qs you might have, feel free to reach out.