Thank you all for your responses!
So to explain a little further, we live in terraced cottages with long gardens. We have two cottages knocked into one, so our garden is quite wide compared to our neighbours.
The half nearest the house had either trellis with ivy growing over it or 5ft fence, so that half of the garden nearest the house felt private. The end half of the garden was always a 2ft wire fence but we have tall plants halfway down our garden so we had an area of privacy and then a grassy more social area beyond this. I don't mind socialising with my neighbours over the fence, but it's nice to have a small area of privacy. I used to breastfeed my first baby on a little seat with the fence behind it, so that I had complete privacy, but now the fence is removed, I am on view.
The neighbours on the other side of my neighbour have low fence for most of their garden so they can also see into our house/garden now too.
They are all in their gardens a lot and we get on well with them all and always chat, but our house and the bit of the garden near our house has gone from very private to exposed.
She sort of 'asked permission' to remove a couple of the fence panels a while back as they were leaning slightly and told us she could only afford wire fence to replace it. I did express concern about loosing privacy and told her I would want to fill the gaps with plants, but ultimately, I couldn't stop her. At the time this didn't seem so bad as it was only a couple of random panels so we still had some privacy from the panels in-between. Just this week she asked to remove a few more panels because they are not in great condition and she wants one long straight low wire fence - this was while the chap was there to put up the wire fence. I had my neighbour and the fence guy telling me the panel had to come down. I didn't feel I could say no, as they are her panels and they were a bit rotten so I couldn't disagree. I went back after speaking to my partner on the phone and said we'd really like some trellis or something there for privacy and we could help pay. She wasn't happy but said ultimately it's up to us what we do on our side and she can't stop us, but she doesn't really like the idea of trellis/fencing as will feel blocked in. I don't think it's a light thing, I just think she enjoys the view of our beautiful garden - adding colour and interest to hers as her garden is just grass. At this point my teething toddler woke up and I had to sort him out. I watched the guy put up the wire fence and my emotions about this just grew and grew as I was sat on my sofa on full view of my neighbours and the neighbours beyond - where I wasn't previously on view!
The deeds don't say who owns what fence - as the cottages are really old and the records all got burnt in a fire many years ago, so we have no idea. According to neighbours it's 'her' fence, as the neighbours have all told us they are responsible for the fence on the left of their house.
I think because I'm pregnant, I am getting over worked up and emotional about this. Also I'd like to be able to get out there and plant/move things myself right now to sort this out, but I'm too pregnant to be digging/planting and my partner hates gardening (I love it but am clueless!)
This aside, we actually get on really well with our neighbour and we have helped babysit for each other and done lots of favours for each other etc. I don't know that fence is viable option for us now due to cost, conflict and also we would have remove/destroy quite a few beautiful mature plants, as there is no longer space for a fence behind them as there is now the wire fence is running along the boundary.
I think our best option is going to be plants that are nearly or will soon grow to around 5ft high. The plants don't have to completely block everything out, maybe 80%? to give me the sense of privacy, and I definitely don't want anything that's going to be huge, invasive or difficult to prune/maintain. I have some red robin and quite like it, though it does require quite a lot of pruning, but I think I could just about manage this. If there's anything else that is similar but maybe doesn't require quite so much pruning, that would be ideal. I also realised today that I could plant things in our garden elsewhere to give some privacy on my sofa which wouldn't need to be as big due to the perspective.
Sorry for the essay! Some of you sounded interested in the story behind this!