Russia's former president was one of the people targeted by the UK in its response to the war in Ukraine.
President Vladimir Putin and his spokesman are among those who will be hit with asset freezes and travel bans.
The UK hit Russia with trade restrictions.
Legislation was passed to speed up and strengthen UK sanctions.
The UK was criticized for being too slow to target Russians with links to President Putin.
The legislation allows the UK to take action against people who have assets frozen in other countries.
The Intelligence and Security Committee of MPs, which oversees the UK's intelligence community, said it hoped the new legislation was the first step in helping authorities ensure the UK is no longer a safe haven.
Two years ago, the committee made it clear in its report on Russian interference in British politics that the UK had been welcoming Russian money for many years with few questions about the provenance.
The Prime Minister of Russia and the Defence Minister of Russia were among the high-profile allies of President Putin who were targeted by the UK.
Russian Foreign Affairs spokeswoman Maria Zakharova, who the UK government called "Russian propagandists," is one of the others.
The UK was going further and faster than ever in hitting those closest to Putin, according to the Foreign Secretary.
She said that they were holding them to account for their involvement in Russia's crimes in Ukraine.
The UK and its western allies have imposed sanctions on Russians since President Putin launched his invasion of Ukraine.
Ukrainian President Volodymyr Zelensky has been issuing increasingly frank pleas for stronger sanctions and western military intervention as Russian shelling of Ukrainian cities exact an ever-higher death toll.
In a video call with Prime Minister Boris Johnson, Mr Zelensky said that it was vital to stop the Russian war machine because otherwise they would come for you.
The UK imposed asset freezes and travel bans on Russian MPs who voted to recognize two rebel-held areas of eastern Ukraine as independent.
Russian vodka and hundreds of other goods were included in the trade with Russia.
The latest package of UK sanctions targeted individuals and organizations with links to the Putin administration.
Some of them had already been sanctioned by western allies, among them Mr. Peskov and Mr. Mishustin, who were described by the US as a top purveyor of Putin's propaganda.
The UK was quicker to sanction others such as Mr Abramovich, who was blacklisted by the EU on Tuesday and accused of benefiting from Russian decision-makers responsible for destabilising Ukraine.
The UK has a list of people who are not allowed to travel to the country.
From 2012 to 2020 Mr. Medvedev is the deputy chairman of the Security Council of Russia.
Mr Medvedev was once seen as more liberal than President Putin, but he warned western nations against sanctions.
He wrote that economic wars in human history often turned into real ones.
The UK government has been accused of moving too slowly on sanctions against Russians.
Many of the opposition parties' assets could be moved out of the UK before they were frozen because of a delay in imposing them.
The Economic Crime Act received royal assent in the early hours of Tuesday. It gave ministers the power to go further, and quickly sanction those who had been targeted by the EU and the US.
The process for sanctioning individuals under previous legislation was frustrating to the ministers.
The Economic Crime Act should make it easier to justify sanctions under UK law.
The UK government added Russian tycoons with a combined worth of more than 100 billion dollars to its sanctions list.
The founder of Alfa Bank was on the list. He has interests in the UK.
While the Ukraine war was a huge tragedy, he said at a London press conference that President Putin would not be swayed by sanctions.
The UK has imposed sanctions on some of the other oligarchs.
Nick Thomas-Symonds is a Labour shadow international trade secretary.
The government needs to make sure the export ban has no loopholes so it has maximum impact.