The government’s anti-corruption tsar, Eric Pickles, is considering naming any foreign citizen subject to a UK visa ban as a response to the inquiry into the 2006 murder of Alexander Litvinenko.

The home secretary, Theresa May, was criticised on Thursday for failing to impose tougher economic sanctions against agents of Vladimir Putin’s regime in the wake of the inquiry’s finding that Putin had probably approved Litvinenko’s murder in 2006. She will meet Litvinenko’s widow next week.

A change in the law that ministers are proposing to Pickles would give the public the right to know who the UK is banning from entering the country, and, by implication, who the UK would let in.

The list would also act as a reassurance for Russian dissidents living in London who fear they may be victims of political assassination. At least two Russian businessmen, Alexander Perepilichny and Boris Berezovsky, who had fallen out of favour with Putin, have died in mysterious circumstances in the UK.

May’s sole substantive measure has been to impose an asset freeze on two Russian agents, neither of whom has any assets in the UK. Both men have scoffed at suggestions that they should come to the UK to stand trial. May is likely to reject calls from Litvinenko’s wife, Marina, to add to the list of Russians subject to visa bans or asset freezes when the pair meet shortly.

There is currently no transparency around the government’s exercise of its powers to impose visa bans or deny entry, all of which are non-statutory, in relation to people involved in serious international crimes such as torture, terrorism and other kinds of organised crime.

Putin’s spokesman criticised the Litvinenko inquiry ruling on Russian television. Dmitry Peskov told Channel One: “I have the feeling that this was for one goal only, to continue turning the spinning wheel of anti-Russian hysteria. And they have been successful. People are becoming zombies, they look at Russians with eyes wide from horror, our bilateral relations suffer and the interests of the British people suffer.”

Pickles is due to publish an update of the government anti-corruption plan before an international conference to be convened by David Cameron in May as one of his main international initiatives of 2016. Cameron said the conference would look at how “to stop corrupt officials or organised criminals using anonymous shell companies to invest their ill-gotten gains in London property, without being tracked down”. He has promised he will prevent London becoming a home for dirty money.

No 10 said the anti-corruption conference would look not just at preventing corruption, but also ending impunity and compensating the victims of corruption. One focus will be on strengthening law enforcement in big international anti-corruption cases, but it will also propose rules requiring disclosure of beneficial ownership of foreign-owned rather than domestic companies.

MPs on all sides of the Commons on Thursday called on the government to do more to crack down on Russian politicians, and their use of London to hide dirty money.

The justice minister Dominic Raab championed the automatic publication of the identities of those subject to visa bans when he was a backbencher, at the end of the last parliament.

He said in the Commons in 2015: “In the 21st century, the British public have a right to know whether the henchmen of despots like Putin – or, indeed, any other international dictator or outlaw – are being granted a free pass to come to this country.

“If we are serious about trying to alter Putin’s behaviour, should we not start by making sure that those who bankroll him cannot enjoy the fruits of their labour here, clandestinely in luxurious comfort?

“Those individuals who bankroll Putin and his like should know that when they cross the line and engage in serious international crimes, their association with him and support for him will bar their ability to enjoy the luxurious Knightsbridge lifestyle that so many of them crave. To ensure that message hits home consistently and publicly, we need transparency over such visa bans.”

He also pointed out that the Home Office does sometimes disclose when someone is subject to a visa ban, but claims it is neither diplomatically sensible nor fair in terms of natural justice to disclose the names as a matter of routine.

In the Commons on Thursday May repeatedly rejected a call from all sides of the House for a “Sergei Magnitsky law” designed to impose mandatory visa bans and asset freezes on any individual linked to the torture and murder of Magnitsky, or similar such international crimes, in Russia and elsewhere. She said she already had powers to impose travel bans.

Magnitsky was the lawyer for a British businessman, Bill Browder, and was brutally killed on orders from the Kremlin for disclosing a $23m (£16m) tax fraud – the biggest in Russian history – that had allegedly been committed by Putin and his associates.

David Davis, the former shadow home secretary, said he backed the proposal of a “Magnitsky” list, with individuals banned from the UK named and identified. “The US has done it, the European parliament has done it,” he said. “We can certainly make it a Europe-wide thing.”

He added: “There is a slight problem with this. Sometimes they [the government] want to ban people without telling anybody, including spies. But I think to have a public list is a good idea. It takes the judgment out of the reach of the courts. I’ve got no problem with a Magnitsky list. I think it’s the most powerful way of doing it.”

Davis renewed his criticism of the prime minister’s low-key response to the Litvinenko public inquiry report, saying that he had “totally misjudged” Putin. He said Russia’s president would interpret the UK’s failure to expel diplomats or impose other measures as a sign of weakness.

The prime minister defended retaining contact with Russia pointing out relations were needed for the Syrian talks to succeed. Speaking in Davos, Cameron said: “Obviously we have real difficulties with our relationship with Russia because of what has happened, and it’s right that we take the action we announced yesterday. But when it comes to Syria, difficult as it is, we have to discuss this issue with them. Because the crisis in Syria will only be solved when all of the players recognise that it’s in their interest to have a settlement.”