No, the fact that he started paying is a pretty difficult argument to counter. I think, in general, if two people negotiate on given terms and then start actin

No, the fact that he started paying is a pretty difficult argument to counter. I think, in general, if two people negotiate on given terms and then start acting as if they had agreement (guy gives him the storage locker, OP starts paying for it) that's pretty good evidence of the contract existing. As far as I understand, this often overcomes some kind of technical problem with the instrument in question. (For example in this case the lack of a signature, only oral agreement.) If it weren't this way, then mutual misunderstanding (for example the actual contract two parties signed is simply flawed or doesn't state what they think it states) would preempt the terms the parties agreed to; moreover, it would mean that you could totally distort the reality of what the parties actually started doing (how they behaved) by narrowly technically reading the paper instead of the agreement. I also think this is the source of common-law marriage: if two people act as if they're married, that's good enough after a while, even if the actual instrument is missing or flawed in some way.