6. Any person who has made a claim for payment under the provisions of the Act, the Secretary of State having determined in relation to that claim that payment should not be made, may apply to the Secretary of State for reconsideration of the determination on either of the grounds specified in section 5 of the Act, namely that there has been a material change of circumstances since the determination was made or that the determination was made in ignorance of, or was based on a mistake as to, some material fact.