My first impression was of those dark trees, on the right in the first 2 photos. Whereabouts does the sun come from. Will those trees shade your garden, or not. Are they your trees. You might need to find out how far their roots extend into the garden. They could make cultivation difficult.
If they were my trees, I'd think of having them down. But dealing with those roots could still be a big job.Do you like the view of that shed in the distance, in the first photos. You could obstruct, or mask, the view if you want to.Cleaning up those paving slabs shouldn't be difficult. I wonder what's under them. Hardcore? You might like to keep the path and just pretty it up.You might be able to make use of those timbers (if they are timbers) to make a raised bed to grow veg, if you want to grow some veg.
I'm sure others will have lots of ideas...
I wouldn't rush to get rid of the trees - in such an open site they add height, structure and possibly provide some shelter from the wind.
Instead, think about what you want in the garden, e.g., types of shrub, bulb plantings, areas of perennials.
Then try planning it around what is already there - that will show you what might be best moved or altered. Work on paper first, though - much better to have a plan before you start stripping things away and find yourself with nothing more than mud to look at.
The garden looks quite long. You could put trellis up to separate it into less daunting areas eg patio area near the house, veg. garden from what looks like raised beds already there and shade garden under the trees at the end. It's hard to tell where the house is. Is it the brick building behind what looks like sheds and, perhaps, a greenhouse? Or is it behind what looks like a stone patio in the last photo?
I think the path looks quite nice and it looks as though someone (you or previous owner was making it and hasn't finished yet.You need to have something to the sides of it because a path going up the middle of the garden makes it look thinner and longer, but it's good that it's not straight. It needs some tidying up, weeding or weed killer and the wooden posts finishing and some more gravel.
If you put up trellis to separate the veg bit you could make a bed with flowers and climbers like clematis and honeysuckle up the trellis.
Anyway, on cold winter days you can enjoy studying the internet and gardening books for ideas.
I forgot to mention the clay soil. Work in whatever you can get, well rotted manure (beg from local stables, farmer?) compost (does your local council have a cheap compost place), leaf mould. Clay is usually fertile, roses are OK with it, but it's difficult to manage for the gardener and difficult for some plants to get their roots through. It can waterlog in the rain and bake hard in the summer. I had it when we lived in the Weald of Kent.
Typical mistake in having the path going right down the middle of the plot.
Still, what you need to ask yourself is what you really want in your outdoor space, before doing anything to it. Make a list of things first, then see if you can fit them in and where.
You could split into 3 sections, formal patio with pots and borders (be carefull with decking as it can get quite slippy with algae), then more structured garden area with curved lawns and cottage garden borders, finally a more natural wild garden at the back. I agree with Berghill about the path down the middle its really not effective. These are ideas and I cant say this is right for your space, thats for you to decide but it will cut down the ammount of work you have to do. Also you might have to check with your local council that those trees dont have a Tree Preservation Order on them, particularly if you are in a conservation area. You DON'T want to be landed with a £20,000 fine (some carry a fine of £2500 just for cutting back without planning permission.
to create some easy ground cover under the trees, hostas and ferns do vers well in shaded areas. You need to know where the shade falls during the day (what direction does your garden face? south etc) you dont want to go to the expense of putting in alot of plants that wont grow because they arent getting enough light. You can talk to neighbours to see what does well in their gardens maybe even take cuttings (especially if they are cutting back anyway). Yours is an end plot so have a bonus of extra light from the side. (how deep is the sewer pipe?)
Wow! what a good size this is and this could be a really nice Garden, I would take your time thinking about the design but like Gary said I think that those trees could do with coming down first.