The government is to protect the savings of British military personnel and civil servants in Cyprus who were facing the prospect of a levy as part of the €10bn (£8.7bn) eurozone bailout on the Mediterranean island, George Osborne has announced.

The chancellor also told The Andrew Marr Show on BBC1 that Cypriot banks based in the UK would be unaffected by the 9.9% levy on savings over €100,000. There will also be a 6.75% levy on savings below €100,000.

The chancellor said: "What I would say about the Cyprus situation is first of all we are not part of the bailout because David Cameron got us out of these euro bailouts when he became prime minister.

"Second, the Cypriot banks in Britain are not going to be included in this bank tax. It is a very difficult situation for people who live in Cyprus.

"But I can tell you that for people serving in our military, people serving our government out in Cyprus – because we have military bases there – we are going to compensate anyone who is affected by this bank tax. People who are doing their duty for our country in Cyprus will be protected from this Cypriot bank tax."

Around €2bn of British deposits are estimated to be held in Cyprus, including accounts for British-born Cypriots, some of the 3,500 military personnel on the island and owners of holiday homes.

Meanwhile Cyprus's parliament has postponed an emergency session due to take place on Sunday to discuss the levy on bank savings. All meetings have been put off until Monday, according to the Cyprus News Agency.

Earlier the Cypriot president, Nicos Anastasiades, had delayed an informal meeting of politicians after growing unrest following the news of the one-off levy.

Cyprus is the fifth country to have asked for aid from the eurozone, but this is the first time a deal has called for savers to sacrifice some of their cash holdings, in what is seen as a dangerous precedent.

The agreement also called for a 2.5 percentage point increase in corporation tax, a bank restructuring and exchanging bank bonds for less valuable equity.

Sharon Bowles, chair of the European parliament's economic and monetary affairs committee, said she was appalled by the Cyprus bailout. "This grabbing of ordinary depositors' money is billed as a tax, so as to try and circumvent the EU's deposit guarantee laws," she said. "It robs smaller investors of the protection they were promised. If this were a bank, they would be in court for mis-selling."

The bailout, agreed by eurozone ministers and the International Monetary Fund, was needed to prevent Cypus defaulting on its debts. The island ran into trouble after its banks were hit by a restructuring of Greece's sovereign debt.

The Cypriot finance minister, Michael Sarris, said after 10 hours of talks which ended with the agreement: "I wish I was not the minister to do this. Much more money could have been lost in a bankruptcy of the banking system or indeed of the country."

But the news led to frenzied attempts by Cypriots to withdraw money from their bank accounts on Saturday.

People rushed to banks and queued at cash machines that refused to release cash as resentment quickly set in. The levy on savers, half of whom are thought to be non-resident Russians, will raise almost €6bn. The move in the eurozone's third smallest economy could have repercussions for overstretched bigger economies such as Spain and Italy.

People with less than €100,000 in their accounts will have to pay a one-off tax of 6.75%, Eurozone officials said, while those with greater sums will lose 9.9%.

The prospect of savings being so savagely docked sparked terror among the island's resident British community. At the Anglican church's weekly Saturday thrift shop gathering in Nicosia, Cyprus's capital, expats expressed alarm, with many saying that they had also rushed to ATMs to withdraw money from their accounts.

"There's a run on banks. A lot of us are really panicking. The big fear is that there soon won't be cash in ATMs," said Arlene Skillett, who lives in Nicosia. "People are worried that they're automatically going to lose 10% [of their savings] in deposit accounts. Anastasiades won elections saying he wouldn't allow this to happen."

She said a lot of elderly Britons had transferred savings to the island when they decided to retire there. "Nobody can understand how they can do this – isn't it illegal? How can they just dock money from your account?" she asked.

In the coastal town of Larnaca, Cypriots described how they had queued from the early hours in the hope of withdrawing deposits from banks.

"A lot of us just can't believe it," said Alexandra Christofi, a divorcee in her 40s who said she had rushed to her bank before doors opened at 6am.

"I had put my money there for a rainy day. It's absolutely all I have and I cannot understand how Cyprus is being singled out. Other EU countries got bailouts and we're only in this position because we supported Greece," she said, referring to the massive losses the Cypriot banking system suffered as a result of Greece's restructuring its debt last year. "Where is the fairness in that? Where is the solidarity and support that is meant to be the reason why we are all unified in this common currency in the first place?"

Maria Zembyla, from Nicosia, said the levy would make a "big dent" in her family's savings and erode investors' confidence. "It is robbery. People like us have been working for years, saving to pay for our children's studies and pensions and suddenly they steal a big share of this money. Russians that currently keep the economy afloat will leave the country along with their money," she added.

Howard Skelton, in Limassol, said: "The only people who will benefit in the long term are the banks. It will be many years before the man in the street begins to feel any benefit from this bailout. The sooner I can return to the UK the better."

The levy does not take effect until Tuesday, following a public holiday, but action was being taken to control electronic money transfers over the weekend. Co-operative banks, the only ones open in Cyprus on a Saturday, closed following a run on the credit societies while ATMs cancelled transactions owing to "technical issues".

Depositors started queuing early to withdraw their cash, and protesters gathered outside the presidential palace. "I'm extremely angry. I worked years and years to get it together and now I am losing it on the say-so of the Dutch and the Germans," said British-Cypriot Andy Georgiou, 54, who returned to Cyprus in mid-2012 with his savings.

"They call Sicily the island of the mafia. It's not Sicily, it's Cyprus. This is theft, pure and simple," said a pensioner.

The IMF managing director, Christine Lagarde, who attended the meeting, said she backed the deal and would ask her board in Washington to contribute to the bailout.

"We believe the proposal is sustainable for the Cyprus economy," she said. "The IMF is considering proposing a contribution to the financing of the package. The exact amount is not yet specified."