Ms Adorabelle,
Knew you were and are being controlled financially.
Your further comments unfortunately do not surprise me in the least. I could see from your initial posting that you were being controlled by him financially in such a manner. Financial abuse is indeed insidious in its onset; this is why it is not readily picked up by the person on the receiving end of such control.
Re your comment:-
"His earnings go into his account first and he transfers some into a joint account. What he does with the rest of his money I have no idea, it's clear that it's none of my business. I've asked him where it goes but he doesn't tell me.
We learn from our parents first and foremost about relationships; the same applies to money. His behaviour re money is a red flag, he is using his greater power and control in this area to further control you. His secrecy is also a red flag.

"He will regularly make big purchases without telling me. We currently have a £500 water softener languishing in the garage that he's had for months and hasn't bothered to fit. Apparently he needs a second bike, despite never riding the one he's got".
Again all pretty much par for the course from a person who is financially abusive in nature. Its alright for him to buy such stuff, it you had bought this there would be hell to pay. Can you not yourself see the double standards he metes out to you here?
"I bank online and can tell you what's in the joint account down to the last penny. I know how much all the direct debits are for and arranged them all to go out on the first of the month so I know what's left. I probably know it better than he does. I think he assumes he has enough to cover everything. I had a budget in mind but got a bit carried away".
Am certain as well that you do (and actually have to) account for every penny. He probably asks you as well. Your behaviour here is characteristic of someone who is being financially abused, this is precisely how people on the receiving end of being financially abused behave.
"We don't get child benefit. It was costing too much in tax so we stopped it".
What the others have explained re this point, do act on their counsel.
"I'm allowed to keep what I earn. It's a pittance compared to his earnings. I usually spend it on the kids. Possibly a small bit of pottery for me. So when I'd overspent I asked him to help out".
How "nice"of him to allow you to keep what you earn. These are all red flags re his behaviours; it is financial abuse. You put the children's needs above your needs as well; that often happens to women who are financially abused.
He indeed learnt this from his own controlling parents; their behaviours as well towards each other was geared to having power and control. Its the same with your H. Your children are being affected by this as well, you cannot fully protect them from his financial abuse of you. I also wonder if he is abusive towards you in other ways as well, verbal abusing towards their spouse is quite common with such inadequate men.
Re your comment:-
"I've tried. I can't make him understand that it's not fair. At least he does put a lot into the joint account and we don't struggle for anything. I don't think he means to come across as controlling, that's just how his parents were. If you'd met his dad you'd sympathise. I can remember when dh and dbil were teenagers, their mum would buy them deodorant etc out of the weekly shop and they'd have to pay her. The exact amount. They were ruthless down to the penny, that lot. A hoarding, what's mine is mine mentality"
He will not change, you can only change how you react to him. His grip on wanting power and control over money will not alter, infact it may further get stronger now. He learnt a lot of damaging lessons from his own controlling parents who were themselves abusive towards their now adult children. Your H has in turn become financially abusive himself towards you. History does have a nasty habit of repeating itself.
I would seriously consider having a chat with Womens Aid on 0808 2000 247 about all this now.