Not really, no. They’re mainly expanded polystyrene which, like many things, can technically be recycled but practically speaking it’s not possible (due to cost, ease, transport, etc etc).
If you take it apart you might have some luck… some councils might take the plastic outer shell, you could reuse the straps or buckles maybe.
Some plastics recycling programs are a bit dodgy in places and if it’s not exactly the right type of plastic in the right condition it might end up on a beach somewhere anyway.
I have seen them used as hanging baskets for flowers!
Otherwise, yeah, council black bin’s your best option IMO. Most reliable way to make sure it ends up in landfill or incineration rather than the countryside somewhere.