I think, rather than redecorating, you'd probably benefit from a slight de-clutter and having new photos taken. Their photographer clearly isn't great, and for a house with this kind of decor the wrong angle, bad lighting, and a poor quality image can make or break it. The living room and kitchen are really your problems... they are the worst offenders and also the first rooms you see.
Living room: The picture with the four faces in the top right corner... take that down or replace with something else. Take the red throw off the sofa as it's competing with the rug (or find a rug with colours that don't clash). Add a couple of well chosen cushions with colours that compliment the room. I'd take the largest plant out of the window too, as it's blocking the light a bit and making the room feel crowded. Remove the pot plant from the mantelpiece, and the large black speaker from the top of the cupboard. If possible, I'd also remove the weird 90's leather sofa (sorry) and replace with two armchairs that are a bit more traditional. Nothing in front of the radiator. I would also arrange something on the coffee table - some artistic books and a pretty candle, something like that.
I can't see what the floor is like in here but it looks grey, which I think is why people are coming for the wallpaper... the wallpaper on its own is nice, but it's warm toned so it doesn't really work with the grey floor, the grey armchair, or the solid black sofa. If there are original floorboards under there somewhere then exposing them could make a world of difference.
Kitchen: Can you repaint the pipes in the corner? The issue is that the boiler, the tiles beneath it, and the cabinets to the side are all at different angles which makes it look like the fitting wasn't done well. Painting the pipes white and removing the magnets from the boiler will make that less obvious. Also remove the speakers from the tops of the cabinets. Some of the pot plants from the living room could be brought in here and arranged on the counters to make it look warmer.
Whoever takes the next lot of photos needs to do a better job with the kitchen because everyone seems confused by it! The first image makes the room look rectangular (one of those funhouse mirror photos which estate agents love and everyone else hates), but it's square in the next, and no pictures of the cooker or anything. It's confusing and makes it seem like you're trying to hide something/present the room as bigger than it is.
I have no issue with the lean-to, but the fact that there are no photos of the inside of it makes me wonder if it needs work, or needs removing altogether. A utility room is an asset, so why aren't you showcasing that? Again, a good photographer could make the world of difference.
The rest of the house is lovely, and anyone who doesn't like the colours can simply buy some paint - no big deal - but many people will have made their decision after looking at the first two rooms. If you were to repaint only one room to try and sell it, I would make it the blue one. It's a bit violent. You don't have to go magnolia, but perhaps a slightly more muted blue. If you can also find wooden chairs that match the table instead of the current officey ones, that would make a difference.
You also cannot market it, or price it, as a 4 bedroom when it's not (yes, even if you have used the study as a bedroom in the past).
It's true that the market is rubbish right now and you have to be realistic. A house is only worth what someone is willing to pay for it. If nobody wants it at the current price then, bluntly, it's not worth that.