Sir Mervyn King, governor of the body, stated he is worried banks in the nation could be at risk should the crisis affect other debt-laden countries such as Portugal and Ireland.
He explained some lenders in Britain have significant exposure to institutions in Germany and France - two nations holding considerable sums of Greek debt.
Speaking to the Commons Treasury, Sir Mervyn - who is also chairman of the Monetary Policy Committee and served as the Bank's deputy governor from 1998 to 2003 - said: "There's sufficient concern in the market about a default for us to think carefully about contingency plans and the consequences of such an event."
He noted there could be as much as an 80 percent chance that Greece might default on some of its loans.
By Asim Shah