I am storing in my shed my summer alloys with tyres. I can source the tyre tower stand or are the tyre covers a better solution. Thank you.

Mr Google says, best to suspend/support them by the rims in some way or if stacking them, sidewall to sidewall is best. out of direct sunlight, and not near any chemicals or electric equipment, not a damp area and good ventilation. If you have a good place the covers are not so important. If there is a lot of dust etc covers are a good idea.
But maybe they are just trying to sell you lots of things so storage will not be a problems if they will wear out from road use in a few years anyway.

I would put a piece of cardboard on the floor of your chosen corner of the shed, stack the tyres side wall to side wall on this and cover with an old sheet. Best away from direct sunlight e.g. a window.

I have read that it is not good to stack 4 tyres/wheels as the side walls may be damaged, what do you think.

If you are concerned then put cardboard or newspaper between the tyres. IMO strong sunlight will do more damage. If you think of the abuse and stresses that tyres get in use I don't think stacking one on top of another will do damage.

Thanks

I wonder where you read that?
My own recent research using Googley and web sites of the major manufacterers like Michelin, Good Year, Continental etc support the tyres on rims should be stored flat/horizontally (wall to wall) and not vertically. I suppose you could periodically change the order in which they are stacked but your back might not like the exercise!

I was always led to believe:

on the rims - stacked
off the rims - upright

edit: another option is hanging them if on the rims (but not off)

There is no problem with storing them stacked. Make sure the wheels and tires are cleaned and thoroughly dry before storage.
Add some air so that they are a little above the normal pressure you use ( +/- 2.5 bar or 35 psi)
Put something on the floor like a sheet of plastic or tarpaulin
Stack them one by one.
Keep them in a cool/dark place and cover with an old blanket or sheet.

Thank you all for your opinions.