If you are looking for part-time work in a more professional job, i.e. a role that helps you develop more career orientated skills and experience – you could try using recruitment agencies. However, be aware that recruitment agencies work on behalf of the employer, not you. This means that when you sign up they will not be searching for a job for you but trying to fill roles for their clients. Sometimes students sign up with a recruitment agency and then feel dissappointed that they hear nothing more from them. You need to contact them regularly to make it known that you are keen and looking for work.
There are many recruitment agencies in London; these websites provide a directory:
To gain a better understanding of how recruitment agencies work and the different types, see: https://www.prospects.ac.uk/job_hunting_recruitment_agencies.htm