As has been said, in England you cannot "make a claim" against a deceased person's estate if they have left a will. Who they leave their money and belongings to is entirely a matter for them.
You cannot contest a will unless you believe it is a forgery, or another later will exists, or the deceased wrote it whilst mentally ill or under duress. Whether you are a child or adopted child of the deceased is immaterial.
So basically, if a valid will has been left and SunnyJim is not among the beneficiaries, that's that.
If no will is left the rules of intestacy apply. For these purposes adopted children are treated as the children of the adopted parents and not of their natural parents.