Welcome,
As regards Mountain house or similar doomfoods, I agree that if you had the space to store the full cans, then this same space may be used to store the empty cans.
Doomfood is a freeze dried granular product, and the empty cans should not contain any residue that is liable to attract vermin.
Mine have a reuseable push fit plastic lid, intended to keep the contents of a part used can fresh for some days. Use these lids to seal up the empty cans as a second line of defence against vermin.

If things got really bad it would be most unwise to discard ANY food packaging where it could attract unwelcome attention.
This applies to other supplies also, spent batteries, empty gas cartridges, boxes that contained candles, empty kerosene containers and the like should not be discarded in any way that could attract attention.