Hi Stinkhorn.
I'm firmly in the anti-
leylandii camp. While it undoubtedly has some value for wildlife, it doesn't have as much value as a native deciduous tree would have in its place, and its negative aspects usually outweigh its positive (in my opinion).
It has its uses, however. In your situation, as it is screening your garden from a public footpath, there is an argument for keeping it, and the case for removing it is going to be influenced by a number of other factors:
1. Garden plans
What do you want to do with your garden in the long term?
2. Shade.
Leylandii casts a very dense shade which inhibits the growth of other plants, and this is usually one of the principle reasons for taking it out.
How badly do those trees shade your garden? I presume the
leylandii in question are the ones in the background of your "feeder" photos? It's hard to tell from those how much of an impact they are having in this respect.
Could you take some more photos? If you could take some from an upper window that show the shade the trees cast at midday, how big they are, and how they relate to the garden as a whole, that would be very helpful.
3. Soil
Leylandii are notorious for parching the soil beneath them of water and nutrients, making it difficult to grow other plants nearby. This seems to be the case with your trees. If you do decide to remove them, you will almost certainly need to improve the soil before you plant something in their place. What is your soil like generally?
4. Diversity
The key to attracting wildlife to a garden is to create a diversity of conditions using a diverse range of plants. A
leylandii hedge is, by definition, monocultural; and, for the reasons above, has a restrictive effect on local diversity in general.
5. Aesthetics
Very much a matter of personal taste. Personally, I consider
leylandii to be a particularly drab and uninspiring tree. Single specimens can be quite dramatic if well-placed within a large-scale landscape, but I think they're inappropriate for suburban back gardens, and I find monolithic, uniform, dark-green blocks of
leylandii hedging deeply depressing. Others may disagree

.
6. Alternatives.
This is where it gets a bit tricky. Nothing grows as fast and as densely as leylandii, which is why its so widely used for screening or shelter belts.
From a hard-landscaping perspective you could, as suggested, fence that side of the garden (either close-board or trellis panels) and grow climbers up it. Done well, that can be very attractive.
From a planting perspective, Silver Birch is a fast-growing native, visually attractive and excellent for wildlife, but won't produce as dense a screen and loses its leaves in winter. Hornbeam or Beech make solid hedges that retain much foliage through the winter, but they take a good few years to mature.
A less conventional alternative is a living willow fence. These are inexpensive, fast-growing, robust, visually attractive and good for wildlife. They lose their leaves in winter, but each year's growth can be woven in to create a solid screen. They require a bit more work and preparation than a conventional hedge, but nothing arduous. I can only find commercial links for this so I can't post any here, but Google "living willow fence" and you'll find plenty of info.
If you decide not to cut them down, you could grow climbers up the trees themselves. If it's sunny enough, Wild Hop will quickly cover a considerable area, supplemented with native Clematis and Honeysuckle. These will all attract wildlife and provide shelter for birds.
Hope this helps
T2