Does anyone know where I can find some very very very strong storage boxes?

[colditz]

ds1 destroys all, and Ds2 helps him.

Ikea trofast

honestly not tough enough, sorry

Do they need to have lids on them? (so kids cant get in)

Have you tried wooden? Maybe something like this...
www.ikea.com/gb/en/catalog/products/20078031

Really. Wow your DS's really are tough

What about trays that are designed for schools?

I've just been looking at military issue foot lockers. They look ideal, but they are also £40 each. they are big though.

They do need to be lidded really, just for adequate containment and stackability. Every stackable storage box I have ever bought has ended up broken, though.

we have been using araldite to glue padlocks and locks everywhere. It's held up so far. Remap suggested it.

Really Useful Boxes used to have a mini parked on top of four of their boxes on their website...

Not sure if that helps?