Qualifications improve your chances; they do not gate the job. Level 6 is the most recognised.
Level 6 most recognisedOpen entry
Your route in
You can start without qualifications - direct entry/volunteering; a qualification improves your chances
1
Starting from scratch
Entry-level courses that feed this route.
2
Qualifications employers recognise (Level 6)
Any of these strengthens your application.
Entry is possible via the Software & Data Foundation (L2) apprenticeship or college (L3) with a portfolio, but a degree (L6) in games design/computing is the typical expectation; progresses to senior/lead designer.