I think at the moment you are feeling depressed because of your situation and its stopping you taking control of sorting it all out as you are overwhelmed by it all. I don't know if this is the answer but am going to make a suggestion which you might want to try or not.
Firstly, if possible try and forget it all this evening and watch a good film on the tv or something. Say tomorrow is going to be the day you make a start on turning your life around and then feel empowered by that.
Tomorrow, make a list of everything in your life that is troubling you and needs fixing, and write down how you want your life to be better. Put it all down on paper.
Then put everything in an order so that the most immediate things that need dealing with are at the top.
Write down a detailed analysis of your finances such as assets, debts, income and expenditure. Write down an income and expenditure budget from now until the end of December month by month so you get an understanding of what months are financially harder than other months and whether you need to work extra hours any month. Take control of your finances. Are there ways of reducing your monthly expenditure by doing things cheaper. Can you increase your income by extra hours, getting a better paid job, getting maintenance from your ex. Just plan it all out. Are there extra things you need to sort out the house. If possible, put by £10 or whatever you can afford into savings.
Involve your children in doing things to help more. They are old enough now to take on a few jobs around the house. I think it is okay to say to them you need help as you are finding it hard to do everything by yourself. I think they might be happy to help you and to feel like they have some responsibility. They can help with cleaning and tidying the house or doing dishes or other things.
Give yourself a year, say, to deal with your list of things that need dealing with. For the first two weeks deal with the most urgent such as the leak and anything need fixing in the house. Over the first month try and tick off four things off your list then each month try and deal with four things at a time on your list.
See what resources there are out there for external support such as Citizens Advice, local church, grants and financial support.
Visit your doctor to discuss how you are feeling and see if there is any support you can get from there.
Consider ways of meeting other people and making friends. It doesn't have to be on a night out. It can be at the park or a soft play activity centre or swimming pool while with the kids. Can you make friends with work colleagues or neighbours. The local church is a good place to make friends and they will have activity things for the kids to get involved in. And you don't really need to be religious to go to the local church. Check out what sorts of clubs and centres there are in your neighbourhood.
Is it possible for you to contact any of your friends just to see if they fancy coming down for a weekend. Don't worry if your house is not looking like a palace. Any friend would not be bothered by that.
Is it possible to reach out to your siblings to close any rift?
Just take small steps at a time OP so it won't be so overwhelming. You will get there, I promise 