The bank also announced that it had decided to keep interest rates unchanged at a historic low of 0.5 per cent.
Economists had been evenly split on whether the bank would choose effectively to print more money to buy assets such as government bonds and corporate debt.
The decision to go over the initial $250bn figure set aside took many people by surprise as a number of recent indicators had suggested that parts of the UK economy were improving.
Surveys from two large UK money lenders had suggested house prices were beginning to rise, while a report on Wednesday indicated that the service sector was growing at its fastest for 18 months.
"This is a huge surprise," said Ross Walker, UK economist at Royal Bank of Scotland.
"All the rhetoric seemed to point to not doing very much more, even up to $250bn seemed odds-against after the better [economic] surveys."
The bank had faced a dilemma at its monthly policy meeting as to what to do with regard to QE.
Halting the process too early could prolong Britain's worst recession in decades, but doing too much risks setting the stage for an inflation surge in several years time.
"While some recovery in output growth is in prospect, the margin of spare capacity in the economy is likely to continue to grow for some while yet, bearing down on inflation in the medium term," the BoE said.
Alistair Darling, Britain's finance minister, who approved the expanded QE programme, said raising the limit would help the bank to avoid undershooting its two per cent inflation target.