The average cost of a paternity test is £200. If a DNA test establishes paternity, then the man in question is billed to cover the cost. In cases which fail to establish “Who’s the daddy”, the state picks up the tab.In some cases multiple DNA testing, funded by the state, never finds the real father.he Child Support Agency is forced to foot the bill for paternity tests when a mother is uncertain who the father of her child is and points the finger at the wrong man. There is no limit to the number of DNA tests a mother can demand in the search to establish who fathered her child.