One of the hardest things about being a single parent is the lonlieness. And yes lots of us have felt this way, and continue to find it difficult.
It is very hard when you have no support, no money for babysitters or going out, and noone to go out with even if you did.
There is no easy answer, but time does make things easier. You do have to give yourself enough time to move on from your last relationship and not try and rush or wonder why you haven't moved on yet. It takes far longer than you realise, but one day you'll find you are there. I've found that the general rule of thumb (1 week for every month you were together) seems about right. That may seem like a long time when you work it out, but the longer you were with someone the longer you do need to grieve for your lost relationship, and future plans, and everything that goes with it. And I promise you that one day you'll wake up and realise you've finally moved on and it doesn't hurt the way it does now.
You also need to try and love yourself and your life as a single person. If you can't be happy alone you're probably not going to be happy in a relationship either. Make time for yourself. That's not always easy if your dc are young, but story time at the library or a play group may give you that little bit of time out the house to stay sane. I used to sit in the supermarket cafe for 30 mins reading a magazine while ds was in the creche there. It was all I could afford. So I'd then get him out and do the shopping together.
Once they are at school it starts getting easier to find a little more time for yourself. Are there any hobbies or interests you have that may lead you to some new friends with similar interest? Even if you can't get to a gardening club or sewing bee, you may find there are groups online. Even playing card games or scrabble on line can help distract you and give you company of a sort and keep you busy.
Is there a gingerbread groups or other groups that meet near you? Just getting out the house can be a stepping stone. I've been going to a lone parent group for many years now. It meets once a month. I don't have much in common with other members there, but it's nice just to get out and chat and have a cup of tea with other adults who know what it is like to be a single parent. And to be able to take your dc with you and know they'll be entertained and have company too. I made a couple of friends through that group and we've been away on outting with the dc and even on holiday on mass as a group. I laugh now when I remember turning up to the first meeting with a book, as I anticipated no-one would walk to me. I've happy to say I've never taken a book with me since.
Be kind to yourself too. I always say that if you didn't manage to be the parent you wanted to be today, then there's always tomorrow. And you did the best you could today and tomorrow is another day. Stay strong and take one day at a time. It's tough, but you can and will manage.