From the article:

Turing even went with the Greenbaum family on
a day trip to the seaside resort of St Annes.
But Barbara recalls it ended badly.

"Alan turned up at our house in a very strange
outfit, which looked like his school cricket
whites. White trousers which came half-way up
his ankles and a white shirt which was very
creased and crumpled. But it was a lovely sunny
day and Alan was in a cheerful mood and off
we went.

"Then he thought it would be a good idea to go
to the Pleasure Beach at Blackpool. We found a
fortune-teller's tent and Alan said he'd like
to go in so we waited around for him to come
back.

"And this sunny, cheerful visage had shrunk into
a pale, shaking, horror-stricken face.
Something had happened. We don't know what the
fortune-teller said but he obviously was deeply
unhappy. I think that was probably the last time
we saw him before we heard of his suicide."

Gee, that's strange...

The inquest decided that Turing had killed himself
using cyanide. A partially eaten apple was by his
side in bed but as it was never tested it's
impossible to say if it was laced with poison as
has been suggested.

Oh really?

An alternative interpretation is that he inhaled
or ingested cyanide by accident during a chemistry
experiment.

So your telling me... That someone with an analytical mind like Turing's... just decided to go waste some money on a fortune teller (because it's not like they're bullshit artists or anything)... while on a sudden, random trip to the sea shore...

And then, he emerges with his mood so visibly shattered, that a young girl never forgets the drastic, unexpected shift in personality, not even decades later does she forget this transient event. A short time later, he's dead. And it's a suspicious suicide.

Someone involved in developing machines to attack german Nazi military ciphers, with years of experience conducting efforts under secrecy with high-level government security clearance, while cities across the channel are being annihilated with firebombing, and futuristic ballistic missiles are falling from the sky.

This man tells a little girl he's going to indulge in a superstitious visit with a "fortune teller", and the liason blanches him white with fear.

That was no fortune teller. He was meeting with some shadowy figure involved in who-knows-what, and was either directly threatened by that person (because of some old-fashioned indignant opinions about his personal life and the respectable nature of his choices, and how they reflect upon his peers) and told that he had crossed an unforgivable line with his indiscretions...

...or he was told some truly disturbing news, maybe along the lines that a leak or a mole was discovered, and that his identity and level of participation in the war effort was now known by dangerous enemies, and his personal safety was very seriously compromised.

In my opinion, the involvement of cyanide seems to favor a professional murder, not a suicide, not mental illness, not bipolar mood swings induced by horomones, not a hobbyist's science experiment gone awry.

I feel that it's entirely possible, given the realm of secrecy and paranoia that Turing operated within earlier in life, that everyone relaxed just a little too much after the war ended, and some bitter post-war animosity had not fully evaporated, and someone knew him or found out about him, blamed him for their wartime misfortunes, and went after him.