Perhaps the advertising for Mini-Milks wasn't quite as successful as it could have been... but once Mum got you to eat one, you were hooked for life.
I'm speaking from personal experience here, Mini-Milks have to be IMHO, one of the most delicious ice-lollies there is. The creamy texture, the sweet taste... oh, the pleasure!

*ahem* Of course, there were many rivals to the icy throne, as mentioned above, strawberry Mivvis, which consisted of an outer shell of strawberry-flavoured ice, filled with vanilla ice cream.

There were Fabs, an ice lolly originally marketed at girls, which were a strange vanilla ice/ice cream thing coated strawberry from one third up, and chocolate and sugar sprinklings on the top third.

The advertising for Cornettos was extremely successful, nowadays one cannot hear O Sole Mio without thinking, "Just one Cornetto!".

As an aside, Zooms have now been "reformulated". They are no longer 95% strawberry ice coated in a thin layer of banana ice-cream in the top two thirds, and blackcurrant ice in the final third. Now, much to my own personal delight, they are nearly 80% banana, with a central core of popping-candy (AKA pop rocks). Deeeelicious.