how many working mums rely on their own mum for unpaid whilst they work?

No our parents are too old and far away to help. I have fitted my work in around dh work as with 3dc too expensive for childcare. Most people I know though with more than 1 dc and small age gaps either had parents helping or were sahp.

My mum does the childcare while I work PT, her mum did childcare for her while she worked FT (before giving it up to become SAHM). Presuming my DC have DC of their own, and circumstances allow at that time, I'd be willing and happy to care for my DGC.

DS goes to nursery 3 days/week, but my mum will do the occasional pick up, or have him for the day on my non-working days if I have something on. Likewise MIL will often have him for an evening if I have work on or a social thing.
My mum still works, so she couldn't look after him all the time anyway - but actually I don't think it would be fair on either of them to have to care for him a lot. They are both late 50s/early 60s, and reasonably fit, but he is exhausting! (just turned 2)
We did consider whether my dad might look after him
(he was a SAHD for me) but sadly he became seriously I'll not long after DS was born and is now very disabled.

Or MIL, not more MIL.

I've never relied on my mother (more MIL) for childcare to work. Both my children went to nursery and now school/after school club (well not ds1 because he's too old for after school club).

MIL recently retired (from working FT), but my mum still works FT (as she has since she returned from mat leave to have my sister in the early 80s). In any case, we live a long, long way from either of them.

Nonetheless, it's usually me that takes time off work for sick children, etc. DH has only fine it rarely when I really couldn't.

Not me. If my parents were nearer & fitter I am sure they would, but sadly not. I pay nearly 1K per month for 2.5 days a week of childcare for my 2 DC. My parents would have loved to help.

My mum and dad pick up dd from school about twice a week. This is a choice they've made - it does help us a lot, but we don't actually need the childcare. DH and I both used to do more pick-ups before they moved, and could do the same again if the need arose.

100%. If my mother couldn't care for DC's I couldn't work. I am on minimum wage, and childcare is expensive in my area.
I luffs my mum I do

I don't, as I have no family nearby but a lot of working parents do use female relatives for free childcare, although one couple did use both parents when necessary.