I am mother of a two children-son aged 13 and daughter aged 12. I am divorced from their father for 10 years and he never tried to contact the children since then and never asked for children's custody or permission to visit them. He paid £250 per month through child support agency for about six months, then the amount reduced to £20 per month, but now it has stopped nearly for a year.
He never asked for children's custody and court did not issue any orders to tell that I have the custody while issuing the divorce.
In these circumstances do I automatically have legal custody of my children or I have to apply for it? If I have to apply for it what do I need to do to gain legal custody letter for my children, who live with me since I got divorced.

I'm guessing you're in the UK - ?

The first question is WHY you think you need a letter? Are you doing something that requires it.

Second question is whether you have contacted the solicitor who handled your divorce. That would be the first place I would go.

I'm not sure how its handled in the UK (ANY question on law needs to include your general locale as laws vary by area. We assume because of the use of the pound sign that you are in the UK), but generally parents share legal custody with one parent designated the primary custodial parent. Unless the court rules otherwise.

Do you know why support changed and stopped? Have you investigated that?

... Second question is whether you have contacted the solicitor who handled your divorce. That would be the first place I would go. ...

And when you get there, ask him or her why custody was not addressed in the divorce decree. Normally that would be the first question you are asked when you tell a lawyer that you want a divorce: "and do you have children together?".