Some £200m of fivers are now dispensed a month, following a campaign to urge more banks to load the notes into ATMs.
About one in eight ATMs operated by UK banks and building societies now hold fivers.
The Bank argued that there was a "strong business case" for banks to load ATMs with £5 notes.
It also said that such a move would be popular with consumers, as many found that these notes were rarely in circulation for long.
The Bank set an aim to raise the proportion of £5 notes dispensed from ATMs from 0.2% of the total value of ATM outflows in mid-2010, to 1.2%.
The latest figures show that this proportion has risen to 1.5%, after changes by ATM operators - including physical and software changes to the cash machines.
By March 2012, over 5,000 ATMs were dispensing £5 notes, with a wide geographical spread, compared with 670 in 2009.
"I am delighted that this initiative has been so successful. A key objective for the Bank is to maintain public confidence in the currency, by meeting demand with good-quality genuine banknotes that the public can use with confidence," said Bank of England governor, Sir Mervyn King.
The Bank also aimed to increase the quality of fivers in circulation, after consumers complained that many were shabby and torn.
In 2012, a total of £4bn in fivers is expected to enter circulation, compared with just over £2bn in fivers in 2010 - through ATMs, bank branches and other sources.
The banks and building societies taking part in the ATM initiative were Bank of Ireland ATMs at Post Office locations, Barclays, The Co-operative Bank, HSBC, Lloyds Banking Group, Nationwide Building Society, Royal Bank of Scotland (including ATMs operated on behalf of Tesco Bank), Sainsbury's Bank, Santander and Yorkshire Bank.
In addition a number of independent ATM operators have started to dispense £5 notes from ATMs such as the Bank Machine, which has set up several hundred £5-only ATMs since 2008.
"Cash is the payment method that best helps the British public budget, and a greater spread of smaller denominations like fivers helps us keep an even closer eye on our spending," said Ron Delnevo, managing director of Bank Machine.
Nearly 10 times as many £5 notes are being dispensed from cash machines than in the summer of 2010, the Bank of England has said.