How likely is it that i would be awarded sole custody of my children:
there is no contact with the father;he tried to commit suicide a few months ago; suspended from work now due to allegations(i don''t know what he has done); makes no payment; any previous contact with children was always insulting talk of mum infront of children ;police have also been involved with several incidents re him harrasing me at work/home..
If you were married when you had your kids or unmarried, but his name is on their Birth Certificate he automatically has PR.
I don''t think you can prevent contact unless the kids would be in danger, which although the situation you describe are not pleasant would not pose a risk.
Is your Ex on any medication to treat depression?
If you made a unilateral decision, he could take it further and CAFCASS would get involved and carry out thorough assessments. From these a Judge can make a ruling for contact. It may be that it is supervised at first.