Neighbours screaming child

[movemamamove]

I'm sure this has been done to death but I'm at my wits end after yet another interrupted night .

Our adjoining neighbour (semi) has 3 children and one screams A LOT and very loud but it's particularly bad at night. I'd guess it's the youngest who is 3 and during the day I can accept it begrudgingly but nighttime is a hideous and it's waking the whole family. Child wakes typically 2-3 times a night (although admittedly the first time is around 10/10:30 and we're usually still up) but it is blood curdling and relentless. Typically 10-15 minutes at full volume and screaming for mummy or daddy which makes me wonder if they go into him or are blindly hoping he'll stop. I feel desperately sorry for them and if they are going in and he's still screaming blue murder I guess there's not much they can do but how do I gently broach the subject? I can't carry on like this for much longer and my teens are doing gcse & a levels and I'm worried how this will impact them during exams.
To give you an idea how loud this is, when it was hot weather and the window were open you could easily hear him 10 houses away (I was at a neighbours for drinks and recognised the familiar wail!!)
Any suggestions of how we can resolve this without making them feel like crap parents?

I don't think you can. However bad it is for you, its far worse for them. Unless you think they're abusing the child (in which case go to social services), you need to put up with it.
No one wants their child screaming in the night when they're trying to sleep. They know it bad, they know its probably bothering others. There's not a lot they can do. If he's only screaming for 15 mins 3 times a night, the odds are that they are doing something. Telling them to do something else, is unlikely to change things for you, but will make them feel worse than they already do and may damage neighbour relations more.

In your position I’d call the council and file an anonymous noise complaint. Some councils can use noise complaints about kids to trigger support pathways that otherwise might not be available.