How old are you and how old are your children, OP? Just to get an idea of timescales (sorry if you've said and I've missed it!)
My marriage ended when youngest was 6. I was mostly single (odd date/brief fling) for 10 years until I met my current partner in my late 40s.
I completely get the loneliness. I had lots of friends, hobbies and an ex who had the children EOW but its still not really enough to build a proper relationship. I was happily single and I enjoyed life but that didn't mean I didn't feel the bone crushing weight of loneliness. Because its not the same. I posted on here at the time and was told I was lucky I had my children and weren't they company enough? Honestly, some people have no idea!
People throw around advice like 'work on yourself' and you feel a bit like 'read the room, why don't you?' But there's an element of it that is true.
It's not that friendships are a substitute for a relationship but that it benefits your MH to have them, which makes you feel better about yourself, you understand yourself as a person outside of 'single mum' and what you have to offer. It also gives opportunities for when the children are older to go out and meet other people.
I reflect on some of my worst periods and can see that while I hadn't caused any of my situation myself, I wasn't helping myself in terms of my thoughts around it.
Someone suggested therapy to deal with your feelings of loss of the life you had. That's not a bad shout. It won't change the reality of your situation but it might help you to feel differently about it. The problem is that, when you're mired in it, you can't imagine that you could ever feel differently. It feels like one problem with only one solution.
It also means that, when your children are older and you are in a position to date, you'll be less likely to hang on to the first man who shows an interest regardless of whether he's worth having or not.
I'm not going to spout trite platitudes like there's someone for everyone or you'll meet someone when the time is right because that's nonsense. But you're more likely to meet someone when you are in a good place. Even if the logistics make it harder for now.