A supplier telling you they are licensed is a claim. The register entry is the evidence.
Finding the register
Most regulators publish a searchable register; a few publish a PDF, and a small number publish nothing at all. Where one exists, every tier-4 record on Gamitas links straight to the entry, not to the home page, because a link that makes you search again is barely a link at all. This matters because the gap between a claim and its evidence is where most supplier due diligence quietly goes wrong, and closing it takes about a minute once you know where to look.
Reading an entry
Four fields decide whether a licence means what you were told it means: the legal entity on the licence, its status, the activities it covers, and the dates. A studio trading as one brand frequently holds its licence through a differently-named subsidiary, so searching the brand alone will often return nothing at all even when the licence is perfectly real and current.