I was surprised to see Gremlins was a 15. Puts it on a par with The Shawshank Redemption.
I've seen scarier Scooby Doos.
There's a report on it on the BBFC site here:
Gremlins
It was reclassified as a 12A in 2012. Looks like it fell on the wrong side of the PG/15 divide in 1984 because a lot of the situations presented were familiar to pesky kids.