The event being described is popularly known as the "British Pet Holocaust." The linked article (and possibly the book it references) leaves out a rather critical piece of information and as a result is a bit sensationalized. On the eve of WWII, the British government formed the National Air Raid Precautions Animals Committee, or NARPAC, part of a larger series of state programs and committees (Air Raid Precautions Department) whose purpose was to protect British citizens and assets from air attack in the event of war. NARPAC was concerned with the welfare of animals during wartime; preventing undue cruelty, dealing with pet food that could also be used to feed people if rationing took effect, finding homes for pets that had lost their owners, or disposing of the bodies of dead pets that could otherwise contaminate water or food supplies that could be used by people.
In the summer of 1939, NARPAC published a pamphlet titled "Advice to Animal Owners." This booklet offered suggestions to British citizens about what to do with their pets should war break out, from sending them to more remote parts of the British Isles free from the possibility of air attack, to euthanizing them if no other solution could be found ("If at all possible, send or take your household animals into the country in advance of an emergency"...."If you cannot place them in the care of neighbours, it really is kindest to have them destroyed"). Many people were also led to believe that if war broke out, the production of dog and cat food would be discontinued as frivolous. As a result, when war was declared by Britain and France on Germany on September 3, 1939, those people that believed they had no other choice did what they had to do, often with great guilt. Well over 12,000 household pets (7,000 dogs, 5,000 cats, and others) were euthanized in London on the 3rd alone, and on September 4, the presumably horrified officials at NARPAC issued a bulletin stating that the production of pet food would not in fact be discontinued. The destruction of household pets unfortunately continued by terrified British citizens who didn't find out about it, especially as the London Blitz began in September 1940.
The London Zoo euthanized all their venomous animals including snakes and spiders as a precaution in case the zoo was bombed and the animals had a potential path to escape. Similar events took place at zoos in Germany and Japan during the war. The Ueno Zoo in Tokyo euthanized nearly one-third of its animals, including especially large or potentially dangerous ones, by various means in 1943 as the war situation worsened for Japan.
Sources:
Bonzo's War: Animals Under Fire 1939-1945, by Claire Campbell
The Nature of the Beasts, ch. 4, by Ian Jared Miller
The British Home Front 1939–45, p. 22, by Martin Brayley
The Little-Told Story of the Massive WWII Pet Cull, by Allison Feeney-Hart (BBC News Magazine, October 12, 2013)