The body responsible for issuing ISO certifications is the Certification Body (CB), which operates under an Accreditation Body (AB). The AB, in turn, is accredited and overseen by the International Accreditation Forum (IAF), ensuring that IAF-certified certifications are recognised as the highest level of validity.
In the UK, the AB is UKAS. For a full list of ABs approved by the IAF worldwide, please refer to the IAF website, linked in the footer of this page.