It could be,
I'm translating a theater drama and there is the main character who is quoting some adverts. The play is set in the 80s.
So if "fairy" is a washing up liquid, the advert make sense to me.
I didn't know what fairy was...
Yes, if the play is set in the UK, I'm pretty sure the reference is to the washing-up liquid. Try googling 'Fairy Liquid' to get an idea of the sort of claims made for it: there's usually a suggestion that it lasts longer/goes further than cheaper brands.
That said, I don't think the phrase is an actual quote from a Fairy advert; it's more like a spoof or take-off