The decision to axe the G8 summit shows Russia faces “growing political isolation”, David Cameron has said.
The UK prime minister said world leaders were sending the “clearest possible” message that Moscow’s actions in annexing Crimea were unacceptable.
The US and UK have said the G8 will be “hard to revive” in the near future.
Moscow has made light of the decision to cancel June’s gathering in Sochi, suggesting the G8 is an “informal club” and members cannot be thrown out.
World leaders are discussing what further action to take against Moscow as they attend a summit on international nuclear co-operation in The Hague.
On Monday, the US, UK, France, Italy, Japan, Germany and Canada said they would meet in Brussels in June as the G7, instead of in Sochi, and Russia would not be invited.
Speaking after meeting UN general secretary Ban Ki-moon, Mr Cameron said any attempts by Moscow to further destabilise Ukraine would lead to significant further sanctions.
“What we have seen at this G7 meeting last night is just a growing sense that if Russia continues to behave like this it will face growing political and diplomatic isolation,” he said.
Foreign Secretary William Hague said it was hard to envisage co-operation with Russia within the auspices of the G8 under current circumstances.
“It’s of course a huge blow to the G8,” he said. “It means there is no G8 this year.
“The president of the United States was very clear in the meeting that it will then be hard to revive that in the immediate future.”
“It would need our values to be clear, our shared values to be clear again and clearly those shared values are not shared by Russia in violating the independence and territorial integrity of a neighbouring nation state.”
The US and EU have imposed travel bans and asset freezes on pro-Russian officials in Crimea and supporters of President Putin after Russia took control of the peninsula.
Mr Hague acknowledged that tougher sanctions, which have been threatened if Russia takes further action to destabilise Ukraine, would have financial repercussions for countries with trade links with Russia but “we have to be prepared to do that”.
“Every country would have to do what is necessary if more far-reaching sanctions were applied, accepting that that would affect different economies in different ways.
“The UK is certainly prepared to do that. There is nothing that other countries in Europe have proposed that we have blocked. The UK is fully prepared to play its full part.”
BBC correspondent Anna Holligan said Mr Hague was keen to stress the economic “leverage” that the EU had with Russia, particularly over energy supplies.