By Jason Douglas And Nicholas Winning 

LONDON--U.K. Treasury chief George Osborne said on Monday that Britain would respect the outcome of the Greece's vote but warned the situation could deteriorate rapidly if an agreement isn't reached quickly.

He also said the U.K. has extended extra assistance to British holidaymakers in Greece as well as Britons who live there following Greece's vote on Sunday on fresh bailout aid.

In the referendum, Greeks voted overwhelmingly against their international creditors' conditions for further bailout aid, in a result that risks deepening the rift between Greece and the rest of Europe and pushing the country closer to bankruptcy and a possible exit from the euro.

The U.K. isn't a member of the single currency and has few direct financial links to Greece, but officials are concerned the crisis there could spread again to other eurozone nations and hurt the broader European economy.

Mr. Osborne told parliament Monday that the risks from the Greek crisis are growing.

"We are urging all sides to have a final go at trying to reach an agreement that defuses the crisis," Mr. Osborne said. He added if there is no signal from Monday's Franco-German summit or Tuesday's gathering of eurozone leaders, "we can expect the financial situation in Greece to deteriorate rapidly."

"It is right that we remain vigilant and monitor the situation carefully, " Mr. Osborne said, adding "we will do whatever is necessary to protect the U.K.'s economic security at this time."

British Prime Minister David Cameron met senior officials including Mr. Osborne and Bank of England Governor Mark Carney earlier Monday to assess the outcome of Greece's referendum and consider whether they needed to respond.

One area of immediate concern for the U.K. government is British holidaymakers and the roughly 40,000 U.K. citizens who live in Greece.

The U.K. Foreign Office has warned Britons to be prepared for travel disruptions and problems withdrawing cash, after the government in Athens imposed capital controls that restrict how much cash is available to EUR60 ($66) a day for withdrawals using cards issued by Greek banks. Foreigners should be able to withdraw more, as long as cash is available. Greek banks remain closed.

On average, some 150,000 British tourists a week are in Greece in July in a normal year, according to government estimates. The Foreign Office advised travelers to take sufficient quantities of euros in cash to cover the duration of their stay, emergencies and any unforeseen circumstances.

Mr. Osborne told lawmakers the U.K. has added extra consular staff in popular holiday destinations in Greece, including the islands of Crete, Corfu and Rhodes, to help with any emergencies.

Officials have also offered advice to some 2,000 British retirees living in Greece about switching their pension payments to non-Greek bank accounts if they are worried they may lose access to their money, he said.

Mr. Osborne confirmed that the Treasury has drawn up plans with U.K. tax authorities to allow British companies facing payment problems from Greek customers to delay paying any taxes that may fall due.

Separately, the U.K.'s export finance agency, which helps firms get loans to export goods and services, said Monday it would no longer process applications to support exports to Greece.

The Bank of England has increased scrutiny of Greek bank branches in the U.K. The BOE said in its twice-yearly Financial Stability Report on Wednesday that the outlook for financial stability in the U.K. has deteriorated in recent days as the Greek crisis intensified.

BOE data show British banks' direct exposure to Greece is minimal: they are owed some $3.2 billion by Greek companies, banks and the public sector, a sum equivalent to less than 1% of their equity, according to the central bank.

Officials are concerned, however, that the crisis could spread to other parts of the eurozone where banks have more at stake, although Mr. Carney acknowledged Wednesday that the eurozone's defenses against such contagion are much stronger now than when the crisis first hit in 2010 and flared up again two years later.

The European Central Bank in March began buying eurozone government bonds to spur growth and stoke inflation in the 19-nation currency union. This move should help to prevent a repeat of the surge in borrowing costs experienced by other nations. The bloc's banks are also in better fiscal health.

Write to Jason Douglas at jason.douglas@wsj.com and Nicholas Winning at nick.winning@wsj.com