How could I quit a part time job?

Well I would not do this, burning bridges is a bad ideal, even if you never plan to go back, this is a on your employment record forever, and employers do check this.

You list your location as London GB where employment law states:

If the Employee has worked for the Employer for MORE THAN one month, the Employee should give ONE week’s notice, unless a different notice period is explicitly stated in the contract of employment.

I suggest that if you want to quit your jobt:

You should post a written letter dated yesterday and hand delivered today giving Notice, and stating clearly what your reasons are. If it is evident that there are good reasons why you will not be able to function efficiently, the employer is quite possibly not going to insist that you actually work your notice.

Employers usually realize that an employee who is working under duress are more trouble than they are worth.

The following link takes you to the UK Employment Law guidance relevant to Notice and Employer is Entitled to:

http://funadvice.com/r/14ohth4fser

– Best wishes - Majikthise.