Just bought a house - can I build a bike garage/shed there ? MS Paint skillz inside

[Gecco]

Please see picture below. red belongs to me, blue to my neighbour.

So the outbuildings to the side of our house are shared. I have a small cupboard at the front and a large space at the back and vice versa.

Now I would like to build a small garage/shed big enough for my bike next to my house - see green square.

Would this be ok or likely to cause problems/not allowed. We have not moved in so cannot speak to my new neighbour about it.

 

[Gecco]

I'm looking at something this size eBay link

Obviously I could just buy that but it would work out cheaper if I build it myself