This is the answer to give, if asked this question in a quiz.
According to Britannica, Hutton was England's first "officially appointed" professional captain.
Over to Wikipedia: "In the 19th century, the captains for overseas tours were chosen by the promoters. The early tours were mostly organised by professionals, especially James Lillywhite, Alfred Shaw and Arthur Shrewsbury. Some amateur–led tours went abroad under Lord Harris and Lord Hawke. Home captains were selected by the home ground authority, who often favoured a local player. [From 1903–4 to 1997, international tours were organised, and the England team was selected, by the Marylebone Cricket Club (MCC).]"
What Wikipedia may be trying to say is that on overseas tours, the promoters would choose the professional organisers (Lillywhite & Co) to captain the England team, and that "the home ground authorities" would choose a (local) professional as captain. But it doesn't actually say this.
Elsewhere, Wikipedia explains that the MCC set up a Board of Control for Test Matches in 1898 (and an Advisory County Cricket Committee in 1904), that these were replaced by the Test and County Cricket Board (TCCB) in 1968, and that the TCCB (along with the National Cricket Association and the Cricket Council) was replaced by the England and Wales Cricket Board (ECB) in 1997. These dates would seem to be inconsistent with those stated above for the time during which the MCC was in control (1903–4 to 1977), but at this point I am beginning to lose patience with Wikipedia, if not the will to live.
Wikipedia notwithstanding however, Britannica's mention of "official appointment(s)" would seem to refer to the time when the MCC was in control – whenever that might be exactly. But it would seem to be safe to say that the MCC was still in charge in 1952, when Len Hutton was appointed as England captain, and that he was the first professional to be appointed since before the MCC took control.
© Haydn Thompson 2024