Your situation is unbearable. You do have 'real' problems - you are desperately lonely and isolated and concerned your children are being shunned socially too. That way of life is unneccessary. Nothing is worth this level of long term unhappiness.
First, you need to get yourself over to visit family and friends this summer. Take leave or even sign off sick - you are actually severely depressed. I have been in that state of mind - crying all the time is a classic symptom. You shouldn't be trying to work in this condition. Take the kids and go somewhere for two weeks where you are liked and loved and known, where your children are accepted and included.
Next, as PP said, look properly at moving. You need to be somewhere you feel at home. How about Chester - you'd be back in England, it's a beautiful town and you'd make friends. As would your DC. Or Liverpool - a friend moved there recently, expecting to be shunned for being a posh southerner and said people couldn;t be more friendly and she loves it. Or Shrewsbury? I'd go for an English town with in reach of north Wales. or a small place on the right side of Manchester.
You need some structure in your life, where you have things to look forward to each week. Can you sign up for an online course that is live - not uni, something unpressurised and fun - film studies or creative writing or an online book club where you get to chat to other people. Can you book some weekends back in England for the coming term, try to hook up with old friends. Are there any fitness classes you could join or running clubs. You don;t have to make friends - don;t even have to try - just be polite but go to help yourself feel better because exercise really does help.
If therapy doesn't work could you try something a bit woo - yoga or meditation to help calm your mind. People who teach these things tend to be a bit more open minded and might be less rejecting of you for being English.
Finally, I would look at getting a short term dose of antidepressants, not to block out your feelings but just to lift you out of the depths of sadness, and then you can slowly come off them once you feel a bit more on an even keel.
I honestly think you can be happy again. By the way, I had undiagnosed PND for four bloody years. Four! It doesn't go away just because you no longer have pregnancy hormones. I needed medication to clear it up. It's possible that happened to you and then it's a vicious circle because people avoid you and you get lonelier.