Hello and thanks for using Just Answer.
I am Al and am happy to assist you with your enquiry.
The cultivation agreement is consent from the electricity company for you to use the land as garden land and which includes tending it and maintaining it.
Just because you are not the legal owner of the land does not prevent you from carrying out your obligation and rights under the agreement. Therefore, just like a Tenant could in a rented property, you do have the right to lop any branches from next door that overhang the boundary, provided these are returned to him next door.
As regards ***** ***** access to the land, this is slightly less favourable- as all you have is a mere agreement to tend the land, you can't legally prevent him from coming on to the land. He would only be trespassing if you owned the land.
Sorry this is not the answer you were looking for in this respect.
Looking ahead, has your partner ever approached the electricity company in the slight hope they may sell the land to her? This would of course make your life easier if you could acquire the freehold.
I hope this assists and answers your question.