Re: UK domestic rubbish collection ...
I suspect a mechanical HDD is unrecoverable after a single compaction cycle.
I once had the opportunity to test the resilience of a 600MB Seagate 3.5" hard drive by putting it under a levelling jack of a JLG 330LRT scissor lift. With a bit of jockeying you can put half the unit's weight on that one jack, so 2.6 ton.
Flat - area would have been about 150cm^2, 200N/cm^2, 200kPa - no deformation
Long edge down - 40cm^2, 650N/cm^2, 650kPa - no deformation
Short edge down - 25cm^2, 1000N/cm^2, 1MPa - a bit of a gap between the case and the lid, platters still spun freely. I've seen drives way worse off still recovered.
Now 20 times that might well be quite damaging, especially if it gets caught the wrong way between the squeezer and something solid. However, the specs for this garbage truck state a press-plate pressure of 35 tons, and eyeballing the plate dimensions I'd say its area is 0.75m^2 (1.5m wide, 0.5m high), so that works out to 48 tons/m^2 or 480kPa, even less than the lift jack pressure with the drive long edge down. If the garbage load is not compacted again after it's unloaded from the truck but going straight into the landfill, the drive will likely be still fully intact. And water, mould and even the chemical residues you could encounter in standard household garbage (discounting aggressive chemicals that should have been disposed of appropriately) are unlikely to sufficiently damage a modern hard drive platter to make it unrecoverable.
The main problem though would be actually finding the drive.
Icon: full chemical hazmat suit with breathing apparatus.