This is what I was coming to say.
He's an addict and I think he needs proper support because an addiction doesn't just go away because you're found out. He needs support to quit in the same way that an alcoholic does. He's swapped one addiction for another.
I don't gamble myself but I know a bit about the gambling industry. You can register with a company called GAMSTOP who will block your DH from being able to register with any casino or gambling site licensed in the UK.
But do you see that caveat? They can only block access for properly licensed casinos/betting sites.
There are quite literally THOUSANDS of casinos and betting sites available online that aren't licensed in the UK. It's not recommended to use them because the regulators aren't so robust but it's not illegal for UK residents to bet at them. They're all on Google etc. Right there. And the thing is, self-exclusion at GAMSTOP won't mean anything because those casinos aren't part of the scheme.
If he is tempted to bet, being self-excluded from UK sites is a very good start and is still worth doing - but he'll still be able to find plenty of casinos to bet at online.
You want to work on this together and give him another chance, so you need to plan for the worst. As an addict, there will be times when he's tempted to relapse. It's the nature of addiction. And if there are sites available, he will still have opportunities.
So my question is - will he have any way of accessing money that he can gamble with without you knowing?
How will you know he's not secretly gambling on unlicensed sites?
How is he going to cope being treated like a child and only given access to money for essentials?
Would he have access to a credit card that he can spend on?
Has he shown you all his statements and bank statements etc yet? Because Experian is only one credit agency and doesn't necessarily have information about everything. (I check my credit file with two different sites and there's info on another one that Experian doesn't show....)
Will he permit you to check his phone/laptop/tablet periodically and without warning so you can check he's not been visiting gambling sites?
I know an acquaintance whose husband was addicted to sex sites and apparently wanted to give up but "couldn't" - so they agreed to some kind of keystroke monitor thing that alerted her if he typed certain words. Don't know her well or exactly how it works, but maybe this is something to consider.
I guess really what I'm saying is that to be absolutely certain he doesn't go back to his old habits, you're going to have to assume there's no trust at all and to check up on everything. No matter what he says now, and no matter how good his intentions are, there's a huge risk that he'll slide back - and you can't afford for him to take you and your DC with him.
It's a big thing to commit to, and quite a change in the power dynamics of your relationship. It's also quite emasculating for him to be treated this way (but it's his own fault) - can he cope with such invasive scrutiny?
I'm sorry love, I don't mean to be the voice of doom and gloom, and neither am I trying to influence your decision to stay or leave. But to be absolutely certain he doesn't fuck your finances more than he already has, these are the kinds of things you need to consider.