Exhibit 99.3

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in the Registration Statement on Form F-3 (No. 333-258749) of Ardagh Metal Packaging S.A. of our report dated February 22, 2024 relating to the financial statements and the effectiveness of internal control over financial reporting, which appears in this Form 6-K.

PricewaterhouseCoopers

Dublin, Ireland

February 22, 2024