Polychlorinated Biphenyls are extremely nasty. They were used as, amongst other things, a non-flammable transformer oil and a basis for paint, from their initial production in the thirties through until their complete banning in the 1970s. They are stable, so don't break down, and they're accumulated in the food chain. One place they are strongly accumulated is cod liver, as in cod liver oil, and speaking as a slack parent who usually doesn't give a monkey's about food scares I wouldn't let a bottle of cod liver oil within ten feet of my children. They're also related to dioxins, which are naturally occurring (or occur in otherwise benign combustion) but are just as poisonous and just as accumulative. PCBs and dioxins, along with mercury, are the reasons why there's a recommendation to only eat farmed oily fish a few times a week.
In practice, the levels are low, but any process which concentrates the waste from fish processing is bound to concentrate anything that fish accumulates: PCBs and dioxins. And farmed salmon gets a lot of its calories from fish oil, and the waste loops back into the oil process.
There are testing regimes and the levels in commercial products are usually low (although there's an active court case in California against fish-oil producers that isn't entirely spurious) and the safe dose for dioxins in children is essentially zero.
There's no plausible mechanism for the claimed benefits of fish oil in children for ADHD etc, so I'm inclined to think it's placebo. You may disagree, but in your putative study of one there's no way to tell and the published studies are utter crap. There is significantly more evidence that the Omega fats are of benefit for long-term cardiac health, and therefore I've been giving it to my children on the basis of placebo for education and more clear-cut long-term benefits for them. I take it myself for the same reason, along with Vitamin C and a few other things.
But: PCBs are nasty stuff. If there were a suggestion that UK fish oils had measurable levels in them, I'd drop the supplements, as the risk of PCB and dioxin poisoning - long-term, accumulative, very nasty, lifetime safe dose very low - are unlikely to be justified by a dubious association with childhood behaviour and a weak association with heart health.
Don't get the idea that fish oil is inherently safe because it's "natural" and "full of vitamins": it isn't. But even if it were, so what - you don't need to eat many polar bear, seal or husky livers to die a lingering, nasty death from Vitamin A poisoning. At the moment, fish oil is probably safe and there may be some benefits: that's a risk/return ratio to keep an eye on.