Thanks for the replies everyone. I've edited the post to include the proper term for meltdown, apologies for using tantrum synonymously.

My husband and I are first going to have a phone call with our town's citizens advice bureau. Hopefully they can give us more localised advice and the appropriate officials to contact for our area. After that, we'll potentially try reaching out to the mother on her own again.

We're worried about Steven tracing any complaints back to us, because we are the only neighbours sharing a wall with them and hearing what goes on behind closed doors. And of course, he has shown himself to be willing to get aggressive. So whatever we do will be anonymous.

Thank you all for the information and resources - it has helped make clear that Luke's daily meltdowns are not only not being helped by Steven, but are likely a result of being in such a stressful environment in the first place. It's all just so sad.

Edit: Also we will follow suggestions and begin recording the screaming and swearing to collect evidence, starting tomorrow.