First step is to obtain the birth certificate. If the deceased is named as the father there is then a rebuttable presumption that the child is his. However, in view of the uncertainty, or if in fact the deceased is not named on the birth certificate, a DNA test would be preferable. If the deceased's body has been disposed of, the sister can probably be used. If the child is his and has not been adopted by anyone else, the child inherits.
However, irrespective of whether the child is the natural child of the deceased or not, the fact that the deceased appears to have been paying maintenance would give them the right to bring a claim against the estate under the Inheritance (Provision for Family and Dependants) Act 1975. Again, if the child has been adopted by a third party this will not apply.