Sorry, I missed your start onto the GW site, so i will say welcome now.
It's amazing how fast things clutter up, isn't it. You must take a look into wood arbours and what Dove said above. There is no need to rip it all out as you really do have the perfect area for what you seek, all you want is a dry warm cover.
How long was it between the first and second photo please as the tree to the top right in the first is growing at a extraordinary rate, in the second! I would certainly try and remove the large, black and white pest in the first pic.
(sorry, Just my dark sense of humor).
You could really make this your own space and not worry about the weather that is just outside. You would be able to become part of it and enjoy all the seasons while covered yet still open to the elements, Look at the sky at night and have your own time to yourself.
Abit of glass of plastic ( god forbid ) on top of the arbour will change your your whole out look on life.
and kind regards
EDIT: Sorry image did not take.
Sorry again as the image is not victorian styled, but i think you will get the idea.