MAY: How Does Your Garden Grow?
A ticket says “Chelsea Show 1935, Vincent Square London SW1”, with the dates Wed 22nd, Th 23rd, Fr 24th of May. Also, a banner outside the Chelsea Show states "The Chelsea Flower Show 1935". In other words: May 1935.
JUNE/JULY: Death in the Clouds
Poirot hands Japp a paper dated ‘Vendredi 5 Juillet 1935’. The same date is shown in the calendar of Inspector Fournier's office.
JULY: The Adventure of the Clapham Cook
The date July 11th 1935 is given on the cheque from Mr. Ernest Todd.
JULY: The Veiled Lady
The housekeeper of Mr. Lavington mentions that Fred Perry won again last year. That means it could be placed either in 1935 or 1936 (according to Wikipedia). I choose 1935 for chronology reasons. Month: July. Hastings states that “anyone might have used the fire”, to which Poirot answers: “In July? I don’t think so”.
AUGUST: The Lost Mine
The man pretending to be Mr. Wu Ling writes the date in the reception book (8/2/35). There is also a cheque dated "27th July 1935" (see below).
I had previously placed this in February, but as Michael very rightly points out in a comment to this post, the date is in August. I take the liberty of quoting him here:
The man checking into the hotel pretending to be Wu Ling uses the American format of placing the month first. This is clear from the date above which is written as '2nd Aug'. Poirot later comments on this, as the date format lets him know that the man checking-in had an American accent (he goes on to say Americans are a "very backward people"). So the episode takes place in August, which makes the cheque at the end of the episode dated 27 July 1935 consistent (Miss Lemon confirms it should have been paid in to Poirot's account 'ten days ago').How I managed to overlook this I really don't know. But I am very grateful for being made aware of the mistake!
AUGUST: Peril at End House
SEPTEMBER: The Tragedy at Marsden Manor
No references. An out-of-office affair, with Hastings, Japp and Miss Lemon. No specific reason for placing it in 1935, other than two newspaper headlines in the paper Hastings is reading: “Mussolini sends his sons to Africa” (Abyssinia Crisis from the newspaper in Problem at Sea perhaps?) and “Perry makes a new record”. Since Fred Perry is also mentioned in The Veiled Lady, I choose to place the story in this year. Moreover, as Michael points out in the comments to this post, Nick Buckley's appendectomy happened on 27th February, which was 'about six months ago'. That points towards August 1935.
SEPTEMBER: The Tragedy at Marsden Manor
Poster in the village states a rehearsal on Wednesday, September 4th. The year 1935 fits the date. Prime Minister Baldwin is mentioned on the radio at Poirot’s B&B. He assumed office in June 1935. A newspaper from Nairobi is dated July 1935.
SEPTEMBER: The Adventure of the Italian Nobleman
One of the letters Ascanio throws into the fire has the date “7 Settembre 1935” written on it. (Another letter seems to be dated “Novembre 1936”, but I choose to ignore that - it's barely visible). The adaptation is probably set in spring 1936, but those months are so full already.
OCTOBER: Double Sin
Poster for Japp’s speech states October 3, Thursday, 8:30 pm. According to the calendar, only the year 1935 fits this date. The actual hotel used for filming was built in 1933.
NOVEMBER: Murder in the Mews
Children celebrate Bonfire Night, and a calendar on Mrs. Allen’s desk states “Tuesday 5 November”. The year 1935 fits the date. Poirot dictates a letter in which he refers to his previous letter of March 2, 1935.
NOVEMBER: The Affair at the Victory Ball
A newspaper is clearly dated November 9, 1935, which means the ball was on November 8. The ball is a celebration of the end of WW1 in 1918, and the date of Armistice Day is November 11, so the date of the ball seems slightly random. Anyhow, the setting of the episode is a close call with Murder in the Mews, set around November 5. But I guess this is just about plausible. Since the producers/writers have decided to change the stage actors into radio actors and use the BBC Broadcasting House, the story has to be set after May 14, 1932 (the official opening).
DECEMBER: The Theft of the Royal Ruby
It’s Christmas. The Egyptian prince is called Farouk and is the son of King Fuad of Egypt. According to Wikipedia, both exist. King Fuad died in 1936, and Farouk took over. The Wafd Party (socialist) in Egypt and the Suez channel are mentioned (conflict with Britain). The Suez conflict is also connected to the Abyssinian War (mentioned in Triangle at Rhodes). In other words, december 1935 would be a probable setting.