oh this is a difficult one.
I would have said it was a no-brainer ie no contract - but now you say he has LD and also that you are a bereaved mother, therefore anxious.... well, I can quite see how you can't cope with them not having credit.
I'm so sorry for your loss. How on earth any mother copes with losing a child I really don't know. You're doing well to be standing, it's perfectly understandable that you are anxious about your kids.
How long is the contract? I'd fight this with T-mobile iiwy - lay on all the details and push and push to get the contract off for good. Contact your MP to put some weight behind it (I'm serious - there are plenty of parents in your position with kids/phones, it's a disgrace that some providers cash in on that grrr). You could go to the papers with this story (which could get picked up by the nationals...).
Then go hunting for a more appropriate package.
I hope I'm not speaking out of turn but my kids went through something awful (a significant and sudden bereavement) and, imperceptibly, I was giving them much more slack than was good for them. It really wasn't good for them, I see that now (hard to see at the time...) and I've learnt that, as hard as it is, it's good to tighten up the boundaries. He may have LD but he still has to learn cause and effect: if he has to 'pay' in some way for this, he'll soon get the message. Either jobs, or something drastic to drive the message home. He has to know he can't do this - the £40 was a warning to you, he was gearing up.
As for £ for household expenses, you can cancel direct debits etc this month - call up creditors and tell them you are putting a hold on direct debits for a few weeks, give them an idea when they will be reinstated. As long as you communicate they don't get out the big guns - creditors are much more forgiving these days (everyone having lean times). This should free up some readies to get you through this crisis. You could also have cancelled the dd to T-mobile before it went out (or would you be charged an extra fee?).
There are also foodbanks, of course (for exactly this sort of situ); crisis loans (which you have to pay back!). But I really think making a big issue over how strapped you are by not covering for him ie not going without food but not hiding how strapped you all are because of his mobile bill (which is true! not emotional blackmail!), will go a long way to getting the message home to him.