On March 4 spy Sergei Skripal, 66, and his daughter Yulia, 33, are found unconscious, slumped on a bench outside a shopping centre in Salisbury.
Speaking on BBC Radio 4's Today programme, Mr Kinnock questioned whether the "celebration" of football should be held in Russian Federation in the wake of the Salisbury poisoning.
Moscow has denied any involvement in the attempted murder of former Russian double agent Sergei Skripal and his daughter.
Earlier today, the British ambassador to Moscow was summoned for urgent talks with Russia's foreign ministry.
Russia's envoy at the OPCW has claimed the substance used could have come from either USA or British stockpiles.
"Russia's behavior on the world stage is continuing to trouble us and we are continuing to press back in meaningful ways", it said, adding that sanctions did not mean the end of the ongoing USA conflicts with Russian Federation. "We are going to continue actions to increase pressure on Russian Federation", the statement said.
"Sooner or later the British side would have to present some kind of comprehensive evidence [of Russia's involvement], at least, to their partners [France, the US, Germany], who declared solidarity with London in this situation", Peskov added.
Russian Federation announces retaliatory measures against UK
Britain's Prime Minister also confirmed that no ministers or members of the Royal Family will attend this summer's World Cup in Russian Federation .
Russian Federation has continued to deny any responsibility for the attack. Alexander Shulgin, Russia's envoy at the Hague-based OPCW, said that Britain and the United States both had the nerve agent.
A source told also Russia's TASS news agency that Moscow terrifying and most advanced Avangard hypersonic strategic missile system could come into service this year. He also cast doubt on the possibilities that the nerve agent was sent through the mail or was placed in luggage that Skripal's daughter brought with her from Russian Federation to Britain.
May warned more measures could follow, noting that the US-led North Atlantic Treaty Organisation alliance and the UN Security Council had discussed the attack, while it was also expected to be on the agenda at a European Union summit next week.
Britain has escalated a war of words with Russian Federation over the incident in recent days.
President Donald Trump joined British Prime Minister Theresa May and the leaders of Germany and France on Thursday to issue a joint statement pinning the blame for the attack squarely on the Russian government.
Britain had only pledged to expel the Russian diplomats after Moscow had failed to explain how the nerve toxin had got to Britain, he said. They remain in critical condition. Police said Glushkov died as a result of a "compression of the neck", suggesting he may have been strangled.
Russian Federation offered some cooperation to British authorities after the 2006 London murder of ex-KGB agent Alexander Litvinenko too.
A British inquiry said Putin had probably approved the murder of Litvinenko, though Russian Federation denied any involvement.