He made the assertion in a letter to NATO Secretary General Jens Stoltenberg today explaining Britain's conclusion the Russian government was to blame for the poisoning.
"Only Russia has the technical means, operational experience and the motive", he writes.
The Skripals were found unconscious on March 4 in the southern English city of Salisbury on March 4.
It was "highly likely that the Russian intelligence services view at least some of its defectors as legitimate targets for assassination", Mr Sedwill said in the letter.
The Soviet Union developed fourth-generation nerve agents known as Novichoks in the 1980s, Sedwill said.
He said it included investigating ways of delivering nerve agents by applying them to door handles.
National security adviser Sir Mark Sedwill said cyber specialists from the GRU - Russian military intelligence - targeted Yulia Skripal's email accounts as far back as 2013.
Alexander Yakovenko, Russia's ambassador to the United Kingdom, dismissed Sedwill's charges as unfounded and untrue.
Meanwhile, Russia's ambassador has accused the British authorities of destroying evidence in the Salisbury nerve agent attack.
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Nevertheless, the attack has prompted the biggest Western expulsion of Russian diplomats since the Cold War, with the UK's allies in Europe and North America concurring that Moscow was either responsible for the attack or had lost control of the nerve agent.
Russia, he said, repeating a claim the Kremlin has asserted throughout the Skripal affair, eliminated all of its stockpiles of chemical weapons in 2017, and as for Novichok, "We did not produce it and didn't store it". It insists that the nerve agent used on the Skripals could easily have been manufactured in any of the other countries that have advanced chemical research programs.
The British government has requested a special meeting with the Organisation for the Prohibition of Chemical Weapons (OPCW) to discuss the findings.
The claims come after the worldwide Organisation for the Prohibition of Chemical Weapons backed Britain's assertion the Skripals were poisoned by Novichok.
But it did confirm Britain's analysis about the substance that had been used.
In the letter, Sedwill said Novichok was found in environmental samples taken at the scene and in biomedical samples from both Skripals and DS Bailey, and that the "highest concentrations were found on the handle of Mr Skripal's front door".
Sedwill goes on to claim that Russian Federation was likely the only former Soviet republic to pursue "an offensive chemical weapons programme after independence".
Britain blamed Russian Federation for the poisoning and Prime Minister Theresa May said the Skripals had been attacked with a military-grade nerve agent from the Novichok group of poisons, developed by the Soviet Union.
"I want to underline: the OPCW only has confirmed the composition of the chemical agent", he said. He said Moscow has "irrefutable information that it was a fabrication".