Factual error: In the House of Commons, Tommy refers to an unseen Tory MP as "My Right Honourable Friend" and as "the member for Epping." The former address is only used for Privy Councillors of the speaker's own party (Tommy is a Labour MP); MPs of other parties would be "the Right Honourable Gentleman." Winston Churchill was MP for Epping at the time and Tommy's secretary later says Churchill is in America, so he can't possibly be addressing the member for Epping.
Factual error: The fact Colonel Younger is black and this may be an issue socially is implied several times (meaning the series acknowledges his ethnicity), but it never seems to be seen as surprising that a black man is a colonel in the British Army in the first place. While there were a small handful of mixed-race junior officers in the army in the First World War, there were no post-war black regular officers (it was actually against regulations at the time) and no black officer would hold such a senior rank until long after the Second World War.
Character mistake: Several times Tommy addresses Sir Oswald Mosley as Mr Mosley instead of the correct Sir Oswald. Mosley never corrects him, which given his snobbishness portrayed throughout the series seems highly unlikely.
Character mistake: Mosley says Tommy won the Distinguished Service Medal. This was a naval decoration. Tommy actually won the Distinguished Conduct Medal. Not a mistake someone like Mosley is likely to make.
Factual error: The on-screen caption when Aberama Gold is in Scotland reads "Glasgow." All we see is rolling countryside, without a city in sight.
Factual error: Several characters refer to "the London Times." It's never called this in Britain. It's just "the Times."
Factual error: Polly refers to Ada's soon to be born child as "the colour of a Hollywood Oscar." The first time that the statue was referred to as an Oscar was in 1939, so Polly saying that was 10 years too early.
Factual error: Mosley is portrayed as forming the British Union of Fascists in 1929 or 1930. In fact, he formed the New Party in 1931. The party failed to win any seats in the 1931 general election (with Mosley himself losing his seat) and Mosley then formed the British Union of Fascists in 1932.
Answer: There has never been prohibition in England. There are many reasons for running an underground distillery. It would be a way to avoid things like government regulations, safe distilling methods, alcohol content limits, taxation, fix pricing, and so on.
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