The UK Misuse of Drugs Act 1971 lists codeine as a Class B drug.

Solpadeine Plus and other over the counter painkillers contain codeine.

How can selling codeine containing products to the public be legal? I don't see any clauses or exemptions for codeine in the Part 2 Controlled Drugs section or elsewhere although I haven't got through the whole thing yet.

Obviously big pharma can apply for licences to produce such drugs, but even at that, the consumer would then be in possession of a Class B drug.

An extract abstract from the Misuse of Drugs Act 1971

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PART II
CLASS B DRUGS

1. The following substances and products, namely:—
[...]
Codeine
[...]

2. Any stereoisomeric form of a substance for the time being specified in paragraph 1 of this Part of this Schedule.
3. Any salt of a substance for the time being specified in paragraph 1 or 2 of this Part of this Schedule.
4. Any preparation or other product containing a substance or product for the time being specified in any of paragraphs 1 to 3 of this Part of this Schedule, not being a preparation falling within paragraph 6 of Part I of this Schedule.

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Solpadeine Plus (to use one brand as an example) contains 8mg Codeine Phosphate Hemihydrate. For any of the chemists here, would that 'version' of Codeine still fall under Class B?

If the part of your post that starts with number 3 lists an exception to the rules, then the misuse of drug act says that salt forms of codeine are legal to posses, and that means codeine phosphate (or acetate or any other myriad of salt forms) is legal.

No, all these paragraphs (1-4) are definitions of a class b drug. So it must be class B then alright!

Edit: But from further research on the hypertron, it would appear that it is legal in quantities of 12.5mg or lower in combination with other drugs such as paracetemol. This is from various unofficial sources online. You think it would mention that in the actual Act.