The right of more than 700 wealthy Russians to live in the UK is under review as the government mulls new ways of curtailing the power and influence of the Kremlin following the Salisbury poisonings.

Home Office sources have told the Observer that ministers believe there may need to be further restrictions on the issuing of visas to overseas investors. This follows a decade when hundreds of well-connected Russians, many of whom are allies of Vladimir Putin and include several prominent oligarchs, have been allowed to make the UK their home in return for investing as little as £1m.

Kremlin critics and anti-corruption groups, who have long complained that the UK has made it too easy for Putin’s allies to reside in the UK, welcomed confirmation of the crackdown.

It comes at the end of a week when Theresa May said the government had concluded that two officers from the Russian military intelligence service, the GRU, were responsible for the poisoning in March of Sergei and Yulia Skripal, an act she said was almost certainly approved “at a senior level of the Russian state”.

The Home Office is conducting a review of tier 1 investor visas, the use of which was heavily curtailed three years ago amid concerns they were being issued to people whose wealth had been achieved by corruption.

Under the changes introduced in 2015, which included raising the investment requirement to £2m, applicants could be asked to confirm the origins of their wealth, something that saw a substantial tailing off in approved applications.

Theresa May tells the House of Commons the Skripal poisonings were almost certainly approved “at a senior level of the Russian state”. Photograph: Mark Duffy/UK Parliament/PA

A Home Office spokesman declined to comment on the review’s findings. But it is understood that the Home Office believes a further shake-up of the visa system may now be necessary as tensions between the Kremlin and London continue to rise.

A Home Office source confirmed that the review, the third in four years, extends back to 2008, when the tier 1 scheme was introduced under the Labour government, which means it involves scrutinising in excess of 3,000 visas, more than 700 of them issued to Russian investors.

The source said: “We are reviewing all tier 1 [investor] visas granted before 5 April 2015, some of which are issued to wealthy Russians. We have not ruled out making further changes to the tier 1 investor route in order to ensure that it continues to work in the national interest.

“The government keeps all immigration routes under review and has the ability to curtail a visa where we find evidence of serious wrongdoing,” the source added.

One prominent oligarch who appears to have already fallen foul of the clampdown is the Chelsea FC owner Roman Abramovich, who withdrew his application for a new visa as relations between the UK and Russia soured.

“We have been calling on the government to reassess recipients of the tier 1 visa to make sure that their entry to the UK was not predicated on suspicious wealth,” said Rachel Davies Teka, head of advocacy at Transparency International, an anti-corruption organisation. “We are therefore delighted that the government now appears to have committed to carrying out these checks.

“During its first seven years in operation, the tier 1 investor visa scheme was wide open to abuse by corrupt individuals as very few – if any – checks were carried out on the source of those investments.”

Davies Teka added: “In this period over 3,000 individuals were granted a visa, each investing a minimum of £1m. Our research found that almost a quarter of those were from Russia, a state associated with high levels of corruption risk. This could mean that over 700 wealthy Russians gained UK residency between 2008 and 2015, without proper checks over the source of their wealth that allowed them to secure that visa.”

The move will also be welcomed by MPs who have criticised the visa system. Writing on the Conservative Home website last week, Bob Seely, who sits on the Commons foreign affairs select committee, called for a change to “our visa regime so we make it easier for ordinary Russians to come here and more difficult for oligarchs, rather than the other way around. At the moment, our visa regimes to too many countries reward kleptocrats and punish ordinary people. Let’s flip this around.”

The visa crackdown is one prong in the government’s response to the novichok attack in Salisbury.

There are claims that the National Crime Agency is looking at issuing a number of unexplained wealth orders to Russians living in the UK, a new form of sanction that could result in some of them having their assets seized.