Are you after something premium? I think there is someplace off J17 that does car storage but is aimed at posh cars so I doubt it will be 'cheap'.

A garage rental would give you space but generally no electric. I think Wilts CC have them in various places but appear to run at about £80 / month, Swindon council ones go about £50.

https://www.gumtree.com/p/garage-par...sey/1312593715

Actually from the advert looks like Wilts CC have moved their stuff over to Aster.