A coroner ruled in 2012 that the spy was "probably killed unlawfully", but also ruled it unlikely his death will ever be "satisfactorily explained".
The police concluded that he most likely got into the bag by himself and died after failing to get out again.
At the same time as his inquest, there were reports that he died in a solo sex game gone wrong, while 20,000 ($45,360) worth of women's clothing had been found in his flat.
Williams was also reported to have visited bondage sex websites and was seen browsing for ladies' clothes at exclusive stores in central London.
Karpichkov, 56, who claims to have a source high up in Russian intelligence services, told the Daily Mail a Russian double agent working at GCHQ set his sights on recruiting Williams to work for the SVR, formerly known as the KGB.
The GCHQ double agent, known as Orion, befriended Williams and introduced him to a third party named Lukas, according to Karpichkov.
Allegedly, Williams' drink was spiked on a night out with Lukas and he passed out.
Photographs were then taken of him in bed next to a man and woman and were used in an attempt to force Williams to co-operate, otherwise his friends and family would see them, says Karpichkov.
Fearing Orion's role as a mole inside GCHQ would be exposed when Williams returned from leave to MI6 the following day, a plan was hatched to deal with the "imminent threat" posed by Williams.
According to Karpichkov, Lukas returned later that evening to Williams' flat, bringing a bottle of wine and saying he wanted to apologise for the "confusion" about his earlier visit.
But the wine had been spiked and after he lost consciousness, he was injected inside the ear with poison.
Karpichkov served in Russian intelligence for more than a decade, reaching the rank of KGB major where he was privy to Kremlin secrets at the highest level.