Neighbours dog barking

[fancyfrogs]

Just looking for advice as feeling at a bit of a loss as to what to do.
The couple who live behind us got a puppy at the start of lockdown. Their garden backs onto ours. When they brought it home it barked non stop in the garden - I didn't mind, I have a dog of my own and all other neighbours have dogs so we all know the score especially with pups.
Fast forward 5 months and the dog barks non stop every single time it is in the garden and I mean relentlessly - it's a small westie type and very high pitched and loud. The owners can be seen standing sighing at it sometimes or say the dogs name gently but don't seem to be doing anything much about it and it is driving us up the wall. These barking episodes can last from a minute or so to about 10 minutes at a time, probably every couple of hours whenever it is in the garden. From speaking to other neighbours we know that it's not just us that it's bothering. DH had been talking to the people who live directly next to them and they mentioned that they've said something to them about the barking twice now but the owners apologised and sort of laughed it off. This morning it was in the garden at 5:45am barking for 5 mins solid, woke us both up and also barks when out at 10/11pm on a night. DH is increasingly concerned as we have a baby on the way and though I know any noise has potential to wake a baby, several prolonged episodes of barking at all hours are beginning to make me worry. We can be sat watching tv with patio doors closed and still hear it clearly. DH was livid this morning wanting to submit a noise complaint to the council, seeing as speaking to the couple has had no effect. I was really not wanting to do this as we have a dog ourselves who occasionally barks (as most do) but granted not to the extent of their dog. I really don't want to upset anyone and would be mortified if anyone complained about my dog but getting to the end of my tether. Thankfully our dog nor any other neighbours dogs seem to retaliate much - there is the very occasional barking war between one or two but other dog is always called in to the house and it stops, while the barky dog continues.
What would you do, what do you think the best course of action is?

[Stellaris22]

I would ask them what training they are doing to reduce the barking and if they have considered getting advice from a behaviourist.

Our dog was very loud as a puppy and we did have a neighbour complain. It was upsetting but understandable, our dog very rarely barks now.

Dogs do bark, but to the extent that this one seems to be isn't ok. I hope they are approachable and try to get professional help for their dog.

[Feralkidsatthecampsite]

Our ndn has a similar yapping thing.. I have been shout to shout Shut That Bloody Ddog Up from my window.
Actually worked!!
They were letting it into the front street before 6 am for a wee!!