Under questioning from reporters at the launch of the Bank's quarterly inflation report, Sir Mervyn King admitted discussions were being held in the UK on how to handle the fallout if the euro collapsed.
In the report, the bank warned of continued risk of a 'disorderly' outcome for the eurozone, as part of its wider forecasts for the UK economy.
Sir Mervyn admitted that the bank could not quantify the most extreme risks from the single currency area and declared that the UK's biggest trading partner was "tearing itself apart without any obvious solution."
As he spoke, investors continued their flight from risk over the crisis.
In addition to the bleeding of value in Greek equities, there has been something of a run on the country's banks as despositors move to protect themselves from a potential devaluation.
As much as 700 million euros (£569m) was reportedly withdrawn in a single day.
The jitters have crossed into Spain and Italy again as the contagion spreads - with the spread on 10 year bonds between Spain and Germany reaching a new record high earlier today.
The euro hit a three-and-a-half year low.
By late morning, the FTSE 100 had lost 0.9% of its value on the day - leaving it at a low for 2012 of 5389.
There were similar falls on the main stock markets in France, Germany, Italy and Spain.
Jane Foley, senior foreign exchange strategist at Rabobank, told Sky News there had been a rush towards the dollar as investors ran from risk and that the latest market moves were evidence of the damage the Greek crisis can inflict elesewhere.
She said: "Over the last two years, firewalls have been put up to try and stop some of this rot but...contagion is carrying on.
"We're very concerned that if Spain does ultimately need a bailout, it might just be too much that the eurozone can bear."
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