Try getting off the pre-pay meter for your gas & electricity as it’ll be costing you more per unit. If you have a smart meter it should be a case of changing the tariff, not the meter itself. I assume even if you’re renting that the energy contract is in your name anyway and not the landlord’s? When I moved to my current home the previous owners were on a pre-pay meter, as it happened with the same energy supplier as me, but it was easily sorted to pay as you go. I opted to pay for what I actually use each month rather than the same amount averaged out over the year because they do take more than they need - when I moved house I had built up nearly £1000 in credit and yet they were actually wanting to increase my monthly DD payment. So that’s when I said I wanted to pay for what I was actually using each month and consequently I didn’t pay anything for ages while they worked off the credit.
And I get why you’re stressing about money, sounds like you have enough for day to day but you’re right, unexpected things do crop up, I have been there myself for several years post divorce. I have only very recently realised I can relax a bit, having built up a decent buffer over several years by only spending on essentials, and never borrowing into next month (I use a credit card but always clear the balance every month). It’s little things that add up - making your own pizza dough is a great example, take a homemade latte to work in a flask instead of paying £3-4 it’ll cost you about 25p, make sandwiches with nice sliced bread instead of rolls, buy supermarket own brands, and things like loo roll, tea bags, detergent, toiletries etc in the biggest size, but check the cost by weight / volume to get the best deal. While it might cost more today than the smaller packs it’s cheaper in the long run - you may already do some or all of these, but you can see what I mean, there’s small savings to be had everywhere. If you can’t afford to buy bigger sizes of products in the shorter term, start with one or two items and gradually build it up so you’re eventually only buying bigger - use your freezer, and meal plan to avoid as much food waste as possible. For activities, depending on how old the kids are, do free stuff like the park, an art gallery, a picnic instead of a cafe, offer to walk a neighbour’s dog, create your own town trail/quiz/treasure hunt for the kids now the weather’s getting better. Try to plan car journeys to keep your mileage down, can you incorporate several errands into one journey, try to use facilities where the parking is free? The old saying about looking after the pennies and the pounds look after themselves is so true. Avoid buying anything on credit, even if it’s interest free, if you can (because the cost of that ‘free’ interest is just hidden the cost of the goods, and it increases your monthly commitments going forward). If you can afford to, pay for things like car insurance and home insurance in a lump sum up front for the year as that’ll also save you a bit.
You don’t mention having any debt, so I think you’ve got this tbh. Use separate accounts as others have suggested to build up an emergency fund pot, one for your known monthly expenses and another for ‘fun’ - cinema, bowling, ice creams, other treats etc that’s an amount you know you can afford after saving for emergencies. Then try to relax a bit. You might find it helpful to look up Dave Ramsey on FB, lots of good advice, you don’t have to follow it all, but it makes sense. Good luck.