All valid points

Just to clarify I had no intention of using the garden fence as part of the structure and would treat the wood before building the greenhouse. But yes that's a good point re the lifespan of the fence.

I am not really keen on the flimsy greenhouses, I think they look nasty.

All things considered I am probably better off getting something like the below:

Greenhouse 6 x 4 Polycarbonate Palram with Base | eBay

If I built something myself I would have much more space but I will just have to get
creative with my use of space.

Well I am glad I posted here, looks like I saved myself a lot of grief. Thanks for all the advice