New neighbours and barking dog

[snookerloopynutsarewe]

Looking for some advice / thoughts please.
We have new neighbours, been in the house about a couple of months, seem pleasant enough though haven't had much to do with them.
They have a dog. The dog is outside pretty much all the time. Every time we open our back door or go outside to the shed or to put out washing the dog barks, and barks, and barks. It sounds aggressive but isn't, it seems quite timid and at first I put it down to nerves, being territorial and thought it would settle down. It hasn't and it's got to the stage that I'm starting to resent it and it's making me angry that I can't walk out of my house or be in the garden in peace. They hardly ever come out to quieten her or take her indoors and they seem to be shutting her up less and less as time goes on.

We have a dog too and he barks sometimes, usually indoors, and we do all we can to keep him quiet. Her rarely barks outside and we don't keep him outside.
What should I do? I know that I should speak to them and I know it will come to that but I don't want to be on bad terms with them and I am a wuss and she is quite formidable. I'm dreading the summer to be honest. And I'm concerned that if I 'complain' and then at a later date we chose to move house I'd have to say that we had a problem with our neighbours and it might be harder to sell.
Has anyone had this and come up with an amicable solution or way of asking their neighbours to keep their dog quiet? Would really appreciate your thoughts.

My bet would be that the dog has chronic separation anxiety, so he's been put outside because he's destructive when left, and barks when outside because he's separated from his humans. It's not easy to solve and they'd need help from a qualified behaviourist.

Does the dog have food, water and shelter outside? If not contact the RSPCA; if it does then they won't do anything.

Otherwise, you're probably going to have to go down the council noise nuisance route. Chances are this will either end with them moving or the dog being rehomed.

@AvocadosBeforeMortgages as far as I'm aware the dog is fed and watered and occasionally walked, although from what I can understand (from conversation with neighbour) it is never allowed off the lead.

I have read up on the breed which is described as aloof and sometimes aggressive and hard to handle, with barking as a common problem. The points you make above do seem quite likely the more I read and observe. The dog barks but it also barks very obviously at me, rather than generally.

I think that I might invest in one of those sonic noise things and see if that stops it a bit. It's clear that they either won't or can't do anything about it and I'm not spending my previous evenings and weekends avoiding going outside, which was what I realised I had started to do.

Another neighbour contacted me this week and asked what I was going to do about too. I know it's a first world problem but it's getting to me.

*precious