I was a child in the 1980's and it didn't puzzle me. Not exactly rocket science, even at a very young age, to know that the two same sized coins meant the same amount, 5p and 10p - and it was explained to me what the distinction was, and the history behind them as well as the word "new", both by my parents and (at some point) at school.
You only need to have something like that explained to you once, and it sticks for all time.
It didn't actually make any difference to anybody, as I recall. Everybody knew what they were and it wasn't an issue. Not even a talking point. It may have confused some foreigners, possibly, but I'm sure they would soon have learnt what they were.
By the way, what you quoted wasn't strictly accurate. He actually said: "However tourists and children were sometimes confused by these strange pre-decimal remnants"