I think people should read the actual report (easily available from the
https://www.btha.co.uk/ website). After numerous pages of discussion, the report includes an appendix which gives a table of all the toys that were investigated.
One commonly recurring thread seems to be that toys are marketed at babies, using images of children that are far younger than 3. But the organization's independent lab determined that these toys were safe only for older children, like 3+ or older. Another theme is missing labeling related to safety or age.
Regarding the helicopter mentioned in the article and commented on by grandparent, in the table it is revealed that the toy was in fact labeled as for ages 3+. Something that breaks easily, releasing button cell batteries, should not be labeled 3+.
The anecdote about the three-year-old girl who almost died due to swallowing the magnets actually revolved around a ten-year-old who the magnets were for. Those should have been accompanied by warning. Unfortunately, that anecdote is just that; it is not linked to anything in the data. The data does list neodymium magnetic balls (item #58 in the AliExpress table) which were accompanied by no safety labels at all (ouch! in spite of magnets being one of the top swallowing dangers: I heard this face to face from an ER doctor). The anecdote about does not specifically identify that product, though, or mention what the issue was (e.g. did the parents not know about the dangers of magnets, and received no warning from the packaging, which could have caused them to act differently, such as closely monitoring the ten-year-old's play with the items and subsequent tidying?)