During my one year master's study in the UK, can I work legally and for how many hours per week?

Yes, you can work legally during your one-year master's in the UK. You are allowed to work up to 20 hours per week during official term time.

During university vacations, you can work full-time. For taught master's programs, the summer period is usually considered term time (due to dissertation work), so the 20-hour limit often still applies.

Your Student visa must permit work, and certain jobs (like self-employment or professional sports) are not allowed.