Every [F1park constable] in addition to any powers and immunities specially conferred on him by this Act, shall, within the limits of the park of which he is [F1park constable], have all such powers, privileges, and immunities, and be liable to all such duties and responsibilities, as any police constable has within the [F2police area] in which such park is situated; and any person so appointed a [F1park constable] as aforesaid shall obey such lawful commands as he may from time to time receive from [F3the Secretary of State] in respect of his conduct in the execution of his office.