23 Provisions as to state or diplomatic immunity
(1) Any state or diplomatic immunity attaching to a person by reason of a connection with a state party to the ICC Statute does not prevent proceedings under this Part in relation to that person.
(2) Where—
(a) state or diplomatic immunity attaches to a person by reason of a connection with a state other than a state party to the ICC Statute, and
(b) waiver of that immunity is obtained by the ICC in relation to a request for that person’s surrender,
the waiver shall be treated as extending to proceedings under this Part in connection with that request.
(3) A certificate by the Secretary of State—
(a) that a state is or is not a party to the ICC Statute, or
(b) that there has been such a waiver as is mentioned in subsection (2),
is conclusive evidence of that fact for the purposes of this Part.
(4) The Secretary of State may in any particular case, after consultation with the ICC and the state concerned, direct that proceedings (or further proceedings) under this Part which, but for subsection (1) or (2), would be prevented by state or diplomatic immunity attaching to a person shall not be taken against that person.
(5) The power conferred by section 1 of the United Nations Act 1946 (c. 45) (power to give effect by Order in Council to measures not involving the use of armed force) includes power to make in relation to any proceedings such provision corresponding to the provision made by this section in relation to the proceedings, but with the omission—
(a) in subsection (1), of the words “by reason of a connection with a state party to the ICC Statute”, and
(b) of subsections (2) and (3),
as appears to Her Majesty to be necessary or expedient in consequence of such a referral as is mentioned in article 13(b) (referral by the United Nations Security Council).
(6) In this section “state or diplomatic immunity” means any privilege or immunity attaching to a person, by reason of the status of that person or another as head of state, or as representative, official or agent of a state, under—
(a) the Diplomatic Privileges Act 1964 (c. 81), the Consular Relations Act 1968 (c. 18), the International Organisations Act 1968 (c. 48) or the State Immunity Act 1978 (c. 33),
(b) any other legislative provision made for the purpose of implementing an international obligation, or
(c) any rule of law derived from customary international law.

Article 98
Cooperation with respect to waiver of immunity and consent to surrender
1. The Court may not proceed with a request for surrender or assistance which would require the requested State to act inconsistently with its obligations under international law with respect to the State or diplomatic immunity of a person or property of a third State, unless the Court can first obtain the cooperation of that third State for the waiver of the immunity.
2. The Court may not proceed with a request for surrender which would require the requested State to act inconsistently with its obligations under international agreements pursuant to which the consent of a sending State is required to surrender a person of that State to the Court, unless the Court can first obtain the cooperation of the sending State for the giving of consent for the surrender.

This provision is wider than the ICC Statute.

Immunity does not prevent surrender proceedings when the person to be surrended is a national of a State Party to the Rome Statute. Further, it allows immunity to be waived in cases where the situation is being investigated in accordance with a UN Security Council Resolution.