When Singh says "an authority on porcelain" does he mean it in the sense of the artistic medium or simply as a type of ceramic?

I ask because the second possibility makes perfect sense in the context of building and maintaining large electromechanical equiment in that era. Porcelain components are still widely used today as electrical insulators in certain high-voltatage applications, and old-fashioned knob-and-tube wiring used porcelain "knobs" as insulators.

In contrast, I can't imagine what use an art historian would have been for a cryptography project, but what do I know about such things?

The thing to bear in mind is that decrypting Enigma messages was only one of the activities at Bletchley Park; it also tackled the 'Fish' teletype ciphers, Japanese codes and other Axis (and neutral) codes, and synthesised and analysed the resulting intelligence. Breaking machine ciphers was a primarily mathematical operation but other tasks such as translation, interpretation and analysis required different skills. Two buildings, Hut 6 and Hut 8, focused on breaking Enigma (Army and Air Force in the former, Naval in the latter), once messages were successfully decrypted they were passed to Hut 3 and Hut 4.

Decrypting a message was just the first step in producing usable intelligence. Messages could be short and fragmentary, only partially intercepted in some cases, packed with technical jargon, in the case of Enigma messages without spaces or punctuation. William Millward gives an excellent description of the activities of Hut 3 in Codebreakers: The Inside Story of Bletchley Park, he talks of intelligence as: "... reviewing known facts, sorting out significant from insignificant, assessing them severally and jointly, and arriving at a conclusion by the exercise of judgement: part induction, part deduction."

The first task of Hut 3 was to divide the solid stream of deciphered letters into actual German messages, identifying possible corruption and filling in missing sections where possible. Then there was translation, usually straightforward but some terms could be troublesome (Millward mentions inventing a place called Senke next to Qatara, though it was actually just the German word for a depression). Translated messages were passed to a military adviser who would determine useful intelligence, cross referencing with an extensive Index to determine if e.g. a location given for a unit was already known, or had changed. The sifted intelligence was then passed on to the wider military, but rewritten to cover its origin.

The various activities required quite disparate skills, obviously languages for translation, Millward also mentions similarities between processing partial messages and solving a crossword. I don't think the skills in chess, bridge etc. directly applied, but indicated the breadth of people involved. Millward mentions that the first wave of people at Bletchley were mainly academics, some earmarked pre-war; he was part of a second wave as the Park expanded recruited from trawling through service records resulting in "... schoolmasters, business men, and odd bodies including an actor." The authority on porcelain was presumably Willie King of the British Museum, Alan Pryce-Jones (Millward's Military Intelligence counterpart in Hut 3) mentions King in his autobiography The Bonus of Laughter ("... one of the chief experts of his day on porcelain - but an eccentric tippler"). Pryce-Jones mentions a few others of the "variety of talents" at Bletchley including Angus Wilson, who would jump into the lake when depressed (fortunately it was only a few inches deep), and Frank Birch, a Cambridge don "... said to be a uniquely talented Widow Twankey in pantomime".

Most of the people you mentioned simply contributed cryptanalytical expertise. Cryptanalysis is a very mathematically heavy discipline. But people who study mathematics, formally or informally, do not always end up in careers using those skills. Everybody needs to pay the bills. Moreover, not everyone who enjoys math "recreationally", as it were, necessarily desires using it for work day to day. Unfortunately there are not a ton of interesting jobs for mathematicians. Depending on class, family wealth, and ambition people with a particular expertise in mathematics or cryptanalytical techniques (which, after all, are very closely related to logic puzzles that people do for entertainment purposes) might end up with any career imaginable. Chess champion is not too far a leap. Someone with many intellectual pursuits who spends a lot of time in academia might be expected to take up chess and if they end up very good at it perhaps make a living from it. But when the government asks for help in the time of a great patriotic war, you are much more likely to whatever it is you are good at that improves the chances of winning the war.

Many diverse pursuits including chess and bridge rely heavily on analytical skills which are very similar to those used in the study of mathematics and especially in cryptography/cryptanalysis. A lot of the folks at Bletchley were brought in from the advice of others there, people who said "you know, that X person is excellent at solving analytical problems like this" and then they were brought in and given some tests and perhaps put to use, some lacked formal education in either mathematics or cryptography.

Asa Briggs, for example, was a historian who focused on the Victorian era (despite having a degree in economics), he was brought in to the Ultra project because he had played chess in college with Howard Smith, a mathematician who was working at Bletchley.

There were several chess champions and chess players. James Macrae Aitken (who earned a PhD but not in mathematics), Conel Alexander (who was a mathematics professor as well), Stuart Milner-Barry (who ended up writing about chess for The Times), Harry Golombek (who was competing in the Chess Olympiad when the war brook out), and others.

Others had more varied careers both before and after the war:

• Daniel Jones was a composer during the 1930s, but he had developed skills as a linguist.
• Angus Wilson was a librarian but knew Italian. After the war he became a writer.
• T.S.R. Boase was an art historian.
• Harry Hinsley was studying history in college when he was recruited into the code breaking effort.
• A. J. Alan (aka Leslie Lambert) was a surveyor and professional magician who became a ham radio operator during WWI and ended up in naval intelligence through WWII, after the war he became a radio broadcaster at the BBC.

I don't know who the "expert on porcelain" was at Bletchley but it's quite likely that porcelain had little to do with their job during the war.