As its unlikely you'll pay any income tax through a part time job, i'd say it's certainly worth the time!
It all depends on what else you'd be doing instead. If it's nothing productive then why not.
If you earn less than Something in £9000 you don't have to pay tax..
If you think about it if you get a part time job and you get like £325 a month, that is like 12 hours a week job. Put this money in a savings money ALL of it since you said you can live without it and after 4 months you already got £1300!
And with that you can buy a car, and then the £325 you get a month you can pay for insurance, tax, fuel and maintenance it definitely is worth it. If you don't want a car save up for a nice holiday or whatever you like!