O.K., here's what the article says:
"Richard Culle, a retired Scotland Yard commander who has been studying the case with Andrew Cook, an intlligence historian, says that a new forensic analysis and an examination of official records helped him to reach his conclusion. "I'm 99.9 per cent certain of this' said Cullen. "There is a fair weight of evidence to show that Oswald Rayner (the british secret agent) was the man."...Now it is claimed that the British security service wanted to kill Rasputin, who was hoping to broker peace between Russian and Germany, because of his influence over the Tsar. The fear, according to Cullen, was that if such a deal had been agreed in 1916, then 350, 000 German troops would have been freed to fight the Allies.
Rayner was known to be in St. Petersburg in December 1916 when Rasputin died. A close friend from univeristy was Prince Felix Yousupov, at whose palace the murder took place.....Yusopov wrote that the day after the murder he dined with Rayner who "knew of our conspiracy and had come in search of news."
The BBC documentary says that modern forensic eveidence contradicts this account. Post-mortem photographs of Rasputin show a mysterious third bullet wound in the centre of his forehead. The precise positioning of this, the fatal shot, suggests that it was the work of a professional killer. It was also fired at close range, yet Purishkevich shot Rasputin form behind at a distance. The 3 bullet holes are of different sizes and forensic scientists have now determined that the bullets were fired from three different guns.
Cullen conludes that there was a third gunman and that this was Rayner who knew about the plot, was at the palace and wanted Rasputin dead. Rayner's involvement was kept secret by his superiors and by the Russian conspirators, who were eager to gain the glory themselves. If Rayner was the killer he never spoke about what he had done. He burnt all his papers and took the secret to his grave in 1961."