The outlook for the UK's financial stability "has worsened" in the light of events in Greece, Bank of England governor Mark Carney has warned.
Risks in relation to Greece include a reduction in the risk appetite of businesses and a knock-on effect on households, Mr Carney said.
But the UK's direct financial exposure to Greece is "minimal", he said.
On Tuesday night, Greece became the first developed nation to fail to make a payment to the IMF.
The International Monetary Fund confirmed that Greece had failed to make a repayment equivalent to about €1.5bn (£1.1bn).
This week, Greece closed its banks and restricted cash withdrawals. On Sunday, the country is due to hold a snap referendum on the crisis.
Speaking at a briefing on the Bank of England's latest Financial Stability Report, Mr Carney said: "Events in Greece have tipped the balance to 'the outlook has worsened,'" he said.
The UK was "relatively well insulated" from the direct consequences of events in Greece, Mr Carney said. UK banks had a small exposure to Greece relative to their capital base, and Greek banks' UK footprint was "tiny".
But he said the issue seemed to be a question of what would happen more broadly to the risks that businesses were prepared to take, and the possible knock-on effects on the wider UK economy.
He added: "In contrast [to direct UK risk from Greece], our economic and financial exposure to the euro area is considerable. Fortunately, the euro-area economy is stronger than a few years ago.
"UK authorities will continue to monitor the situation thoroughly and will take any action necessary to safeguard UK financial stability."
Greece could exit the eurozone, and possibly even the European Union, if an effective resolution to the debt crisis is not found.
There are two crucial meetings scheduled for Wednesday afternoon to discuss whether to give Greece access to emergency funds.
European Central Bank (ECB) officials will decide whether to grant an emergency loan to Greece.
And Eurozone finance minsters will discuss Greece's latest proposal for a third bailout.
Meanwhile, Greece's Prime Minister Alexis Tsipras has offered new concessions to the country's creditors.
On Tuesday, eurozone ministers refused to extend Greece's bailout, cutting access to billions of euros of funds. The ECB also froze its liquidity lifeline to Greek banks.
Hours later, Greece missed its deadline for the €1.5bn payment to the IMF.
In July, Greece faces debt repayments of about €8.03bn to its creditors. The cash-strapped country will need to refinance €3bn of six- and three-month Treasury Bills, pay another €3.5bn for a maturing bond held by the European Central Bank, and meet a €450m loan repayment to the IMF.