Theresa May is being pushed to ho head to head with Moscow in a move which will likely enrage the Kremlin.
Senior politicians and Lords are attempting to introduce laws imposing visa bans on anyone known to have committed serious human right abuses.
A “Magnitsky Act” could be used to stop people entering the country, although, there are cases where this already happens.
Former Prime Minister David Cameron insisted Britain should follow the US and Canada and make official a law which can ban people currently free “to come and go from Britain as they please”.
In a speech last week Mr Cameron said: “One of my regrets of my time in office was that we didn’t introduce the Magnitsky Act.
“The Foreign Office argument was that Britain’s existing approach was better, because we could sanction all the people on that list – and more besides. And I went along with it.
“But I soon realised this ignored the advantages of working together – with other countries – under a common heading.”
In the Lords Baroness Kennedy, the QC and human rights campaigner, is bringing a private member’s bill to reject individuals “known to be or to have been involved in gross human rights abuses.”
Former Justice Secretary Tom Tugendhat and senior Labour MP Ian Austin are leading a similar, popular effort.
Mr Tugendhat said: “Corrupt states are spreading their poison and we must act to stop them.”
Vladimir Putin has personally fumed over the US bringing in laws, and hit back.
He banned adoptions of Russian children by US parents after it was pushed through, leading to a list of names subject to asset freezes and visa bans.
The Magnitsky acts are named after Sergei Magnitsky, a lawyer who was killed in prison while investigating a giant fraud against his investment firm, Hermitage Capital.
Bill Browder, a British financier is pushing for the ban.
Mr Browder said: “The fact that Britain is so far behind the US and Canada needs to be fixed.”
Baroness Kennedy said a list of people subject to the ban would be published, something which is necessary to “both focus the attention of those applying that law and introduce greater transparency into the exercise of the power to impose visa bans.”
On Friday Baroness Kennedy said of Magnitsky’s death: “Knowing that Russia under Putin will never prosecute those who jailed, persecuted and ultimately killed Sergei, Browder has lobbied and campaigned and urged other nations to deny sanctuary to his killers and to create laws which will deny those criminals the enjoyment of travel, the use of ill-gotten gains and the anonymity that which allows them to escape ignominy.
“So far, he has persuaded the United States and Canadian Governments to legislate, and it is time that we did this, too.”
The move is likely to cause tension between Boris Johnson and Sergey Lavrov as Johnson heads to Russia as Foreign Secretary for the first time in five years.
During his visit a debate on “Russian interference” ill be held in the Commons.