Hi there,
There a number of resources to secure a part-time job while you pursue your Masters in the UK. Birmingham’s cost of living is relatively low compared to other big cities like London, so that is helpful. I am not sure if you will be able to meet all your living expenses from working part-time as it depends on a lot of factors such as: your current skill set/hireability, the amount of time your studies allow you to work part-time, the number and kind of jobs in the market and the number of hours they are able to let you work (especially keeping coronavirus-related economic effects in mind), and lastly the quality of life you would be pursuing. This includes rent, bills, food, travel, entertainment, shopping and so on. I would recommend you to err on the side of caution and be prepared to cover at least 50% of your total expenses out of your own pocket. It may be possible for you to work 10-12 hours per week, but it is usually harder to secure a job that offers 20 hours/week. I wish you luck with your endeavors and hope this was helpful! Take care, Appy