The size of the cut - the most dramatic since 1981 - signals the Bank's concern the UK is heading for a long recession.
It follows an emergency cut in rates last month from 5% to 4.5%.
However, banks are expected to take their time deciding whether to pass on the cut to mortgage holders and savers.
The cut was followed by the European Central Bank lowering its eurozone interest rates from 3.75% to 3.25%.
The interest rate cuts come as the IMF predicts that developed economies will contract for the whole of the coming year for the first time since World War Two.
'Bigger than expected'
BBC economics editor Hugh Pym said: "The Bank of England is using terms like 'very marked deterioration in the outlook' and 'severe contraction'.
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 This cut... should help to ease conditions in the credit markets, and allow banks to pass the benefits on to their customers 
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"It is clearly very concerned about the possibility of a prolonged recession in the UK.
"The risks of high inflation have now evaporated, and because the bank is worried that inflation will now fall well below its target, it has felt the need to come up with this cut, which is much bigger than expected."
Mortgage fears
The hefty cut will reduce monthly repayments for those with tracker deals - an estimated 40% of mortgage holders - by about £134 on an average £150,000 mortgage.
There have been some concerns that a cut in the Bank of England's base rate might not be passed on to other borrowers.
