Foreigners who do not have a status of residence that allows them to work are basically not allowed to work in Japan, but by obtaining a Permit to Engage in Activity other than that Permitted under the Status of Residence Previously Granted, they will be able to work for a short period of time (28 hours per week in principle). Also, if you want to engage in activities other than those permitted by your status of residence, you can apply for a Permit to Engage in Activity other than that Permitted under the Status of Residence Previously Granted. You can apply at the Immigration Bureau and usually get the result in about two weeks to a month after you apply.
I myself had a part-time job when I studied in the UK. There was a limit of 20 hours per week. The income was very helpful to make ends meet, and I learned a lot and made more friends by working.Our office can represent you in the application process for permission to engage in activities other than those permitted under the status of residence, so please feel free to contact us.