Using a reverse auction, the Bank bought just under £2bn of the bonds, known as gilts.
The amount of offers the Bank received from commercial banks was about £10.5bn, meaning that financial institutions wanted to sell five times more debt than the Bank had offered to buy.
There were no bidders for the non-competitive portion of the auction, where bidders commit to selling the debt to the Bank without setting a price.
Analysts said that was most likely due to the unprecedented nature of the auction, with banks unwilling to commit themselves until they have seen whether the competitive potion of the auction was successful.
Similar auctions will continue twice weekly.
The policy, known as quantitative easing, has never been tried previously in the UK.
The hope is that those who sell the government bonds will use the money from the Bank to lend to individuals or companies or invest in business activity.
The prices of long-term government bonds, or gilts, have surged 20% over the last few days in anticipation, which has resulted in yields on the benchmark 10-year bond dropping to a record low.
The BBC's business editor Robert Peston said the drop in the cost of borrowing appeared to be a "triumph" for the Treasury, which has to sell over £100bn a year of new government debt to finance its budget deficit.
"The device of authorising the Bank of England to buy up a huge proportion of these IOUs [the government bonds] has apparently reduced the cost of all that borrowing to an astonishing degree," Mr Peston said.
These actions are unprecedented in the Bank's 315-year history, but are now considered necessary as interest rates approach zero and deflation becomes a growing possibility.
It has government permission to inject a further £75bn into the economy if it wishes, after slashing interest rates to a record low of 0.5% to boost the UK economy, which has entered a recession.
Deflation - or falling prices - is bad for the economy as it encourages consumers to delay spending in the expectation that prices will soon be lower, potentially worsening an economic downturn.
The governor of the Bank of England, Mervyn King, has admitted he does not know how long quantitative easing will take to have an effect but says it will "eventually work".
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