Commercial leases? That would be me!
You are not entitled to put this pump anywhere except in the property which you “leased”. Therefore, if this pump is outside the property on the edge of another piece of land which may be sold, not only is your responsibility to move it, the landlord can compel you to remove it (until it has been in place without consent of objection not in secret for 20 years).
The existing lease of the shop may not be in your name but when you purchased the sandwich shop, you should have negotiated the assignment (purchase) of the lease at the same time.
The purchase of the business and the purchase of the lease are normally conditional upon each other so you don’t get one without the other and vice versa. This is what solicitors do when you buy a business.
Alternatively if you simply brought the limited company (if it was a limited company) then the lease and the business drag along with the shares that you purchased. You haven’t mentioned a limited company, so I assume that is not the case.
It doesn’t matter that the landlord’s brother fitted the pump if you do not have the consent of the landlord.. Anything that is fitted to the building becomes part of the building the landlord is still at liberty to ask you to remove it if it is a tenants addition.
I disagree that you have any security. There was supposed to be an assignment of lease and that was always intended and you have not done that. Therefore, I am of the opinion that you have a licence/tenancy at will which only the view could terminate on reasonable notice. The existing lease is presumably still in existence and what you want to do, in my opinion, is to negotiate an assignment of that immediately.
The argument you are going to have is whether the rent that you paid was on the old lease or under your informal licence. You don’t meet me to tell you now that this has been done very badly.
If the old lease has expired there was a statutory right to a new one provided it is not opted out of the 1954 Landlord & Tenant act. So there is quite a bit of legal work to be done here.