I think the fact you were in care yourself should not cause any problems with adoption, assuming you have worked through it all.
I think the abusive ex may present more of an issue. If you have had counselling you may find that you are able to stop ex being emotionally/ verbally abusive to you. Have you done the Freedom Programme with women's aid?
Is your ex abusive to your child? Are there any safeguarding issues?
If not, and your adopted child would have no problems or contact with ex, it may be fine but you would still need to show you have worked through all this and your existing child can cope with the changes too.
As a single parent adopter you'd be supporting two children alone, do you have room in your home and money to do this?
You'd need a spare room for new child, not sharing with your existing child.
If this is something you really want to do, you could find out all the steps needed to get in the right place for this.
Can I ask if you work and how flexible it is is?
Also how old your child is and how long ago you and ex split up? You do not need to answer these.
Don't abandon your dream of adopting but I think thus may be something you could do in the future when boundaries with ex are fully in place and have been for a long while
Also, when you have a support network, relatively flexible work, a home big enough to accommodate two children in seperate rooms and your child is old enough to not need you too much so you have capacity for a younger child.
If all this is in place now, I would speak to social services but still advise caution to ensure your child has recovered from any fallout from your and ex's break up.
Good luck.