Almost every food supplement sold in the UK carries a batch (or "lot") number somewhere on its packaging — it's a legal traceability requirement, not an optional extra.
Where to look
It's most commonly printed or embossed on the base of the bottle, or on the back or bottom edge of the label, usually alongside a best-before date. It's often a short alphanumeric code rather than a long serial number, and it may be printed in a different way from the rest of the label — inkjet-printed rather than part of the main artwork, for instance, since it's added at the point of packing rather than at the design stage.
Why it's worth knowing
The batch number is what connects the specific bottle in your hand to that production run's records — including, where a brand publishes them, its certificate of analysis. Without it, there's no way to confirm that a given test result actually applies to what you're holding.
If you can't find a batch number on a bottle, or a brand can't tell you which certificate corresponds to it, that's a reasonable thing to ask about directly.