This is the view laid out in a report written by Credit Suisse analysts, which estimated that Barclays has around Â£40 billion ($60.9 billion) worth of exposure to Spain and Portugal.
The Credit Suisse paper forecast that RBS has up to Â£35 billion of exposure, mainly in Spain, but also in Greece and Portugal.
Howard Wheeldon, of BGC Partners, told the Guardian that the problem is not just confined to British banks, especially if Greece defaults.
"The pressure will then be felt and exerted on national banks that hold the Greek debt," he said.
Mr Wheeldon added that "very many" German, Swiss and French banks are exposed to the debts of the country at the moment.
"It just may be that with so many banks involved one of these might just go down," he warned.
Earlier this month, it was revealed that Greece's budget deficit stands at a higher-than-expected 13.6 per cent of gross domestic product.
By Asim Shah