As Russian oligarchs are useful idiots in the power games between the greater powers, minor agents like Alexander Litvinenko are used and later discarded when they become an embarrassment.
Andrei Lugovoi, the Russian politician, had had links with both Alexander Litvinenko and with Boris Berezovsky who himself was a darling of the Yeltsin administration. However, when the anti-Russian intentions and Chechen connections of Berezovsky became all too clear, Andrei Lugovoi wanted none of it and distanced himself from people that he understood were traitors. Andrei Lugovoi's love for Russia made him an obvious target.
Events were working very much against Litvinenko and Berezovsky. Since 2001, Britain had been involved in Afghanistan and British soldiers were dying on Muslim soil killed by Muslim fighters associated with Islamic extremists in Chechnya. The Blair administration found itself caught in a contradiction. On the one hand, war criminal Tony Blair wanted to help the enemies of Russia and on the other he couldn't possibly justify any kind of support for people who were friends of those killing British soldiers in Afghanistan.
Despite his political interests, Alexander Litvinenko's father wanted to return to Russia and Litvinenko's involvement with Berezovsky who was wanted for crimes committed in Russia was a natural obstacle. Here comes the twist in the story. The Russian government was aware of Litvinenko's father desire of returning to Russia and this is why they sent Andrei Lugovoi to London to ask Alexander Litvinenko to provide them with the necessary paperwork to make Boris Berezovsky position in Britain untenable.
Russia had been asking for Boris Berezovsky extradition for a long time and the British Establishment would not agree to extradite Berezovky who was also a CIA operative facilitating ways of escape for other operators, including relatives of deposed politicians, to evade prosecution. The same legal firm that worked for Berezovsky was involved in helping Russian criminals to settle down in Britain.
The sole possibility of Alexander Litvinenko reaching an agreement to help his father was a worrying scenario and the British Establishment decided to get rid of Alexander Litvinenko and this was done for two fundamental reasons. They had to protect Boris Berezovsky whose activities could become a serious political embarrassment at a time when Britain was at war in Afghanistan and to allow the continuation of anti-Russian activities. Naturally, to cover up the real motives for the assassination, they blamed Andrei Lugovoi and used the whole affair in the dirty war against Russia.
Boris Berezovsky, having lost his right-hand lieutenant, was becoming weaker and his usefulness in the war against Russia - Berezovsky himself had publicly stated that he wanted to bring down the Russian administration - was becoming a thing of the past. Berezovsky was loosing influence and finally lost his money in a dispute with Roman Abramovich. So, Boris Berezovsky became a notorious nuisance and the British Establishment got rid of him too. Firstly, they tried to make the public believe that Berezovsky had killed himself because he was extremely depressed having lost his power and his money. Later on, the news came that he had a string around his neck and after that no more explanations were given and in fact no explanation would have been necessary because nobody cared about a man whose political days and influence were over.
Russia had changed and Britain was involved in several conflicts in Muslim countries including Afghanistan (2001) and Iraq (2003) and the influence some operators had was a thing of the past.
Marina Litvinenko - Alexander Litvinenko's widow - has repeatedly claimed the obvious: that Alexander Litvinenko was working for British Intelligence Services, something that British Intelligence Services have continued to deny. To sum up, Alexander Litvinenko was used by British Intelligence Services and was killed by British Intelligence Services when he became a liability for the Blair administration.