"The British ambassador will be summoned to the Russian foreign ministry on Saturday", TASS state news agency said, quoting the foreign ministry.
Mr Putin has cast his country as a fortress besieged by hostile Western powers with him as its defender, and state media is likely to portray the anti-British move in that context.
The foreign ministry said Moscow's measures were a response to what it called Britain's "provocative actions and unsubstantiated accusations".
The statement said the government could take further measures if Britain takes any more "unfriendly" moves toward Russian Federation.
Mr Bristow, speaking to reporters after being summoned, said the United Kingdom would "always do what is necessary to defend ourselves, our allies and our values against an attack of this sort".
Britain's Foreign Ministry said it had anticipated Russia's response and its priority now is looking after its staff in Russian Federation and assisting those who will return home. The British diplomats have a week to leave.
Russian Federation has complained that Britain has failed to provide any evidence of its involvement in the Salisbury attack and has said it is shocked and bemused by the allegations.
Russian Federation has denied the U.K.'s allegations, accusing Britain of using the incident in a campaign to smear Moscow.
On Friday, Kremlin spokesman Dmitry Peskov said statements by British Foreign Secretary Boris Johnson tying Putin to the attack were "shocking and unforgivable".
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On Friday, police said they were treating the March 12 death of exiled businessman Nikolai Glushkov as murder after a post-mortem found he died from "compression to the neck".
"Make those conventions work so we rid the world of chemical and biological weapons".
However, she said Britain had "no disagreement with the Russian people".
It said the move was a response to Britain's "provocative actions" and "baseless accusations over the incident in Salisbury on March 4", referring to the poisoning of Sergei and Yulia Skripal with a nerve agent developed in the Soviet Union, which Britain has blamed on Russian Federation.
Sergei Skripal, 66, and his daughter Yulia, 33, were found slumped over and unresponsive on a park bench on March 4 shortly after they left an Italian restaurant in Salisbury.
A British policeman was also poisoned when he went to help them and remains in a serious but stable condition.
Moscow has denied any involvement in the attempted murder of former Russian double agent Sergei Skripal and his daughter. Russian officials had previously said that Russia had destroyed the Novichok weapons when it had dismantled its chemical arsenal, which was completed previous year.
The Swedish and Czech foreign ministers and the Slovak foreign ministry all separately rejected the Russian claim.
Ms Bishop said Australia supports a thorough investigation into the poisoning of the Skripals.
British Prime Minister Theresa May said Saturday that her government will consider its next steps against Moscow after consulting with Britain's allies over the next few days.