It's basically another way to say that you will give someone a call later on, like when you get home or have some free time.

The origin of the line 'you and your m8 where bunking off school,right, and you were enjoying ur 99p bargain mcflurry on ya local council bench, when all of a suddenly your other m8’s nan appears after a quick trip to the local tescos (supermarket) down the road, and you have a quick chit chat. And right before she is about to leave she says “I’ll give your mum a tinkle later” and walks off like a fuckin ledge.'

Got the covid-19 vaccine