Prime Minister David Cameron said a eurozone banking union should not discriminate against those countries who do not use the single currency.
He told reporters at the EU summit in Brussels that changes within the eurozone affect Britain as they "affect the organisation that we are are part of".
Mr Cameron also reiterated that Britain will not become a eurozone member, adding, "Certainly not while I'm Prime Minister anyway".
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"We've never actually spoken so publicly about her," the Duke of Cambridge said. "But we felt that this was the right time to do it."