My daughter was the same, didn't talk at all. I suspected autism but her pediatrician basically laughed at me. She is actually now on the waiting list to be assessed after 4 years of me fighting for it.
She's 5 now and talks, but that was after speech and language failed and just made her lose confidence (it's better in other areas), we had portage which was also useless. When she still wasn't talking at gone 3 I started baby sign, which was very hard as she didn't point, wave or follow instructions. But eventually she managed to sign for food, drink, nappy and bed, and she signed I love you, which was the best thing ever since I didn't think I'd ever actually hear her say that.
The best thing I did to try and help my daughter talk was no longer use sentences with her, I'd shorted everything down a lot. So instead of "are you hungry" or "do you want a drink" I'd just say "drink" or "hungry" and shorted all my sentences down to 2-3 words and repeat myself a LOT. I got lots of pictures books like "first 100 words" etc, and we'd sit down and I'd point at each thing and name it, she liked that and took a liking to some objects in there and pages more than others.
It took a lot of work and patience, and a lot of fighting for people to listen to me. But now she's 5 she talks all the time, she doesn't always understand how to put a sentence together properly, and she still can't follow some basic instructions, and her speech is the same as, if not a bit behind her 3yo sisters. But I thought she'd never talk and it's amazing how far she's come.
I think your son shows some similar signs of autism to my daughter, maybe it could be worth going for an assessment?
It's hard on the NHS especially as they hardly listen to you, and they look for things like eye contact which my daughter is good at, in fact she does it too much. If you can afford it you can go private though.