The move by the UK, the US and the EU over the weekend means the Central Bank of the Russian Federation (CBR), the Russian National Wealth Fund and the Ministry of Finance of the Russian Federation will struggle to access cash reserves.
It led to the rouble dropping more than 20% against the dollar and could have fallen further if not for the central bank raising interest rates from 9.5% to 20% on Monday.
Central banks typically hold reserves overseas in dollars and other major global currencies.
The sanctions mean Moscow cannot access those funds which the central banks could have used to prop up the country’s currency.
They also cannot issue new government bonds to raise fresh money because international investors are unable, or unlikely, to take on Russian debt.
Mr Sunak said: “These measures demonstrate our determination to apply severe economic sanctions in response to Russia’s invasion of Ukraine.
“We are announcing this action in rapid co-ordination with our US and European allies to move in lock step once more with our international partners, to demonstrate our steadfast resolve in imposing the highest costs on Russia and to cut her off from the international financial system so long as this conflict persists.
The governor of the Bank of England, Andrew Bailey, said: “The Bank of England continues to take any and all actions needed to support the Government’s response to the Russian invasion of Ukraine.
“We welcome the steps taken today by the UK Government, in co-ordination with EU and US authorities, as an important and powerful demonstration of the UK’s commitment to the international rule of law.”
The new rules also stop anyone in the UK processing any financial deals or transactions for the Russian central bank and wealth funds or various Russian banks.
It stops Russian companies from raising fresh money from international investors to refinance debt – although few are in desperate need to renew their bonds, which typically run for several years before needing to be repaid.
Mr Sunak added that further sanctions could be imposed, including banning Russian banks from accessing the Swift financial system, used for transferring money between banks globally.
All eyes are on Russia’s energy sector and whether sanctions could be imposed on the industry.
The EU still relies heavily on Russian gas and oil, with gas prices up 20% on Monday and oil back above 100 dollars a barrel, having fallen at the end of last week below the psychological milestone.
The Bank of England will also be closely monitoring the situation to see what impact it could have on inflation, with some economists predicting it could rise higher than current predictions of 7.5% and stay above 6% for the rest of the year.