What skills have you got, and how marketable are they?
Outside of my full time job, I do;
Consulting: working with international companies looking to move into UK markets, earns about £100 a month.
Event work: Registered Paramedic, standing around doing nothing at football/racing/rugby/ music events, £20p/h (limited to weekends due to main job)
Frontline work: Registered Paramedic, 10-12 hour shifts whenever I want, paid at £25p/h. Downside minimum 10 hour shift (usually 12), actually hard work.
in short, to bring in an extra £10k a year, you’re going to have to work very hard and save a lot too. fitting that round your life will be a challenge, and tiredness is a real issue, especially if hours are flexible and you’re chasing the cash.
Easiest gig is probably Uber, but costs could out weigh earnings unless you work a lot of unsocial hours.
Teaching would be my choice… music lessons, tutoring kids in maths/science/English whatever. Assuming you’ve got the skills and patience?