OK, are you sitting comfortably? Right, in the opening scene we saw Trevelyan and someone else in an Egyptian tomb blowing it up and presumably making away with the contents. Well Trevelyan ends up killing that someone who was a curator or something for a local museum I think.
The curator's wife never gets his body as he goes missing. He was hidden in the tomb. At the same time Trevelyan returns to Britain leaving behind a woman he has gotten pregnant. The woman is the sister of the man he killed and because she is a single mother she is seen as an outcast by the rest of her family and thrown out onto the streets of Cairo. She dies three years later leaving her son on his own.
He grows up and becomes quite a resourceful and ingenious man; he decides to travel to Britain to avenge the death of his mother and perhaps his Uncle.
Trevalyan goes to the local hotel to marry the young woman because her name is Violet; the pregnant woman he abandoned in Cairo was also called Violet.
Trevalyan books a room under the name Frank Airwell which wotshername works out to mean F.Airwell/farewell. This is a sign he expected to die that day. It is thought that Jim's drunken manner and arrogance along with the supposed letter from Trevelyan, his guardian, cutting him out from the will gives Jim a motive for murder. In fact Burnaby uses this fact to frame Jim once or twice whilst Burnaby helps "investigate" the murder.
When Burnaby and Jim's fiancee get to Sittaford House, Trevelyan's agent realises the Turkish Delight was poisoned, killing his hawk although Trevelyan was the intended target. Since the phones aren't working, the agent makes the 2 hour walk to the hotel to warn Trevelyan his life is in danger.
After a while Burnaby also leaves Sittaford House to help the agent and in doing so provide himself with an alibi. Burnaby doesn't actually walk, he uses some skis to ski down the hill; this takes less than two hours. As Burnaby reaches the hotel, he is spotted by the English doctor who would later blackmail him and get killed for this. His body being placed next to Jim in the pantry to frame Jim again.
Burnaby enters the hotel though the cellar which was left open because the so-called chef is actually the escaped prisoner. The hotel owner dismissed his staff so that his cousin could escape prison and hide at the hotel. So Burnaby enters the hotel and finds his father's room. Goes up and meets his father. Trevelyan says, "Who are you?".
"It is a wise man who knows his son" comes the reply. Trevelyan expresses delight at meeting his long lost son, who promptly knifes him. Burnaby plants Jim's lighter to frame him and hides his ski boots up the chimney.
Burnaby then leaves, circles back on the agent who, being an ex-soldier, almost strangles him in self-defence. This gives Burnaby the alibi that he needs.
Several things catch him out. When he moved the skis outside Sittaford House ready to use later, he forgets to shut the window he used. This wakes Jim's fiance and Miss Marple. Miss Marple deduces that someone opened this window and forgot to shut it.
Also Trevelyan married the young woman who was in the bathroom when he was murdered. She hears someone cough. This is Burnaby lighting a cigarette so that there is more evidence to frame Jim.
It also transpires that the servant at Sittaford House is Eygptian and is the companion of the widow of the bloke Trevelyan killed in Egypt. They tracked him down to kill him to avenge her husband's murder. See he was killed in 1925 and in 1950-2ish his body is discovered in the tomb which has been looted. The widow was the single woman at the hotel.
Matthew Kelly played a Whitehall dirt-digger. He was tasked to delve into Trevelyan's past; Trevelyan was in with a chance of being Prime Minister and Whitehall wanted to check he had no skeleton's in his cupboard; to be honest the skeleton was in a tomb in Egypt so Trevelyan was clear on that one.
Think that is all, anything else just ask.