Before the book
The Fat Man was a rival of the Falcon (real name Henry von Falkenberg) but he was greedy and wanted his money. He plotted how to get his money. The Falcon had hidden his money away in capital cities in safes, in the form of diamonds, and the Fat Man was especially interested in the London safe because it was the biggest sum.
Then the Falcon died. He told his manservant, a dwarf named Johnny Naples, about where the diamonds were and how to open the safe. Naples flew to England and got into London, where he found the safe. He just didn't know how to open it, not being English, so he did some research and wrote down what he found. Johnny Naples was being spied on by the Fat Man, as well as the two killers William Gott and Eric Himmell, the two German assassins. But before they could get him, Naples was killed by an intruder.
In the book
The Fat Man sent Tim Diamond a threatening note telling him to meet at three p.m. at Trafalgar Square. He arrived dramatically, and became apparent that he was an anorexic man - his name was a joke, but he did use to be really fat. However, his doctor told him to shed weight, which he took to the extreme, eating only yoghurt and losing 70 pounds. So, he made a deal. He wanted the dwarf's parcel, which turned out to be Maltesers - and this made no sense, why would the Fat Man want Maltesers if he was on a diet? He even poisoned the pidgeons as he went with poison corn.
The Fat Man attended the Falcon's funeral, and he sent his chauffeur to raid the Diamond brothers' flat. But the chauffeur was killed by Gott and Himmell. Then, the brothers were arrested, after the Fat Man held them up and threatened them with death.
Later, Tim was in jail for false crimes and Nick, his younger brother, went to the dwarf's hotel, but the Fat Man threw a grenade in which bought the whole place down. He was trying to kill Nick especially.
The Fat Man then had his thugs break into Nick's flat and grab him when he appeared. The Fat Man took Nick down to the Thames and tried to drown him by putting him in a bath full of cement where he'd sink. The Fat Man told Nick about the Maltesers and how they opened the safe with their bar code number. Then he tried to kill Nick, but was interrupted by police. He ran off.
Nick got all the gang together in the cemetery and explained the situation. He told the Fat Man and the Germans about the safe. Then the criminals began to kill each other in greed. Himmell shot the Fat Man and the Fat Man shot Himmell. Then the Fat Man realized he'd been shot, and they both fell to the ground.