About 50 mourners saw Russian ex-spy Alexander Litvinenko buried amid claims a contact of his was now in a coma.
Mr Litvinenko's father Walter arrives at a mosque to pray for his son
His wife, son and parents attended North London's Highgate Cemetery, where an imam said an "unscheduled" prayer.
The former KGB agent's death on 23 November, in London, has been linked to the radioactive isotope polonium-210.
Meanwhile, Russia is investigating the attempted murder of Mr Litvinenko 's contact Dmitry Kovtun. A lawyer known to the ex-spy said he was not very ill.
Mr Litvinenko's coffin, a dark-stained Jacobean oak Garratt casket, was supposed to be laid to rest in a strictly non-denominational ceremony.
But after Mr Litvinenko's father Walter had spoken at his graveside - watched by Mr Litvinenko 's wife Marina and the couple's son Anatoly - an Islamic associate of his Chechen friend Ahmed Zakayev interrupted and performed a Muslim prayer.
Earlier, mourners, including Mr Litvinenko's father had joined Muslims for midday prayers at the Central London mosque in Regent's Park, where a funeral reading was given.
Alex Goldfarb, one of the former spy's closest friends, described it as an "unfortunate detraction".
He said: "It was supposed to be a non-religious, non-denominational ceremony according to the wishes of the widow."
Chechen separatist Zakayev, who was a friend of Mr Litvinenko, had also attended the reading, along with exiled Russian billionaire Boris Berezovsky and filmmaker Andrei Nekrasov.
Mosque representative Ghayasuddin Siddiqui said Mr Litvinenko's body could not be brought to the mosque.
Mr Zakayev had said earlier this week the body would not be taken to the mosque because of concerns about the radiation it contained.
Mr Litvinenko's father had said earlier this week that his son had requested before his death to be buried according to Muslim tradition.
But his closest friends said they had "strong reservations" about the suggestion.
After the burial service, a "solemn and dignified" memorial service was held in a private function room in Lauderdale House on the other side of Waterlow Park.
Mr Kovtun met Mr Litvinenko at the Millennium Hotel in Grosvenor Square, London, on 1 November. Hours later Mr Litvinenko fell ill.
Russia's Interfax news agency said Mr Kovtun fell into a coma after being questioned by Russian investigators and Scotland Yard detectives.
"By the doctors' diagnosis, Kovtun's condition is critical," the agency said.
However, Andrew Romashov, a lawyer, said Mr Kovtun's condition had not deteriorated since he met the prosecutors.
"Kovtun's condition is satisfactory," he said, dismissing the earlier reports as "provocation".
Earlier, Russian prosecutors said they were investigating what they are treating as the murder of Mr Litvinenko and the attempted murder of Mr Kovtun.
A statement from the prosecutor's office said checks had established Mr Litvinenko died as a result of poisoning from a radioactive substance.
It said Mr Kovtun had suffered an illness connected to poisoning by a radioactive substance.
In another development British authorities played down the risk to health after small traces of a radioactive substance were found at the British embassy in Moscow following a precautionary check.
Officials said the levels of radiation found would not pose a risk to public health.
In London, Scotland Yard confirmed it was treating Mr Litvinenko's death as murder.
"It is important to stress that we have reached no conclusions as to the means employed, the motive or the identity of those who might be responsible for Mr Litvinenko's death," a statement said.
The British embassy announced on 4 December it would test one of its rooms as a precaution, after former KGB bodyguard Andrei Lugovoi visited the building to deny any involvement in the poisoning of Mr Litvinenko, 43.
Mr Lugovoi and Mr Kovtun reportedly met Mr Litvinenko at the Millennium Hotel. Mr Lugovoi is also expected to be interviewed in Moscow.
Russian officials are expected to conduct the interview but British detectives will be in attendance.
Nine Metropolitan police officers are currently in Moscow but have had restrictions placed on their investigations into Mr Litvinenko's death by the authorities.
Russia's chief prosecutor, Yuri Chaika, said British officers could not arrest Russian citizens and suspects would not be extradited to Britain.
Tests have been carried out at a number of venues Mr Litvinenko visited in London on that day.
Earlier, Mario Scaramella, the Italian academic who also met Mr Litvinenko on 1 November - at a sushi bar - was discharged from hospital in London.
Mr Scaramella was under observation after testing positive for polonium-210.
Friends believe Mr Litvinenko was poisoned because of his criticisms of the Russian government, but the Kremlin has dismissed suggestions it was involved in any way as "sheer nonsense".