I'm recently diagnosed ADHD with an ADHD daughter. I've not read what others have written, What works for one person doesn't work for others. Here are my thoughts on your lad.
Are the school aware you think is has ADHD? How many conversations have you had with the Senco? Teachers are rarely trained in it, but are generally willing to support it. That being said supports are cheap. I've split mine into tools and behaviours. Tools are things like noise cancelling ear plugs (Loops are amazing though I use a knockoff set that were £4 on Amazon), privacy screen and Google tasks. Behaviours are things like remembering to use my tools, taking frequent breaks, micro rewarding (I'll get a brew/grab a biscuit/use the loo/scroll Facebook etc once this task is finished), telling people when they are distracting me...politely most if the time.
ADHD folk tend to be event driven not time driven. Deadlines are rubbish, but say I need this done before I can do this other thing, and I'm there. Again behaviours.
You need to talk to school. Tell them you are certain he has ADHD, and that you will be sending in noise cancelling ear plugs and you require that teachers remind him and allow him to use them. Likewise, he needs support to remember what homework he has.
You need to talk to him about what ADHD is and means for him. It is very common for ADHD folk to suffer anxiety particularly around failure and rejection. My daughter's temper is so much better since we brought that out into the open for her. She can now recognise when someone is pushing those buttons or if a situation is affecting her.
She's well aware of what her ADHD brain can do, we've talked a lot about what works for each other. She's 10. She came into the kitchen the other night...mum, you do know I can see 6 jobs on the go here that you've started, your ADHD is showing...and walked off. She's still learning to manage hers, but I think the most valuable skill I can teach her is to speak up. She needs to demand her accomodations and justify why she needs them. I can't be there all the time to do that for her. I think you need to work with your son to accept that he thinks differently and that he needs to advocate for himself.
Do lots of reading about what ADHD is and how to help manage it.
Lastly, look at the ADHD.co.uk website specifically the bit about right to choose. Ask school to document what they are seeing, and take that and observations to your GP and ask for a referral stating that you want to use the RTC pathway.
It's ok to be an ADHD person, we just need to learn to manage in a world run by neuro typical folk. We've been adapting for them for generations, they're only just beginning to realise that a few simple accomodations and behaviours can make our lives so much more harmonious.
Apologies if this is a bit curt...I'm trying not to write too much in one splurge.