It says polymer notes are cleaner, more secure and - because they last longer - £10 million a year cheaper than the cotton paper currently used.
The proposals could see new-style £5 and £10 notes starting to replace paper currency for the first time in the Bank's 300-year history.
If produced, they would also be smaller, in line with other countries, with the £10 reducing in size to become slightly larger than euro notes.
A consultation on the change will include events at shopping centres across the UK to allow members of the public to feel polymer bank notes and give their comments on whether they are in favour.
Concerns about the notes being slippery and possibly sticking together, and that they would not fold as easily as paper, have already been raised by focus groups which the Bank has been holding since last summer.
Retailers, banks and the cash industry have also been asked for their input.
Meanwhile, a study by the Royal National Institute for the Blind found a 50/50 split on preference for paper or polymer, with most saying they could get used to the plastic.
New Bank governor Mark Carney introduced plastic notes two years ago in Canada while in charge of its central bank. He said earlier this year before starting his current job that Threadneedle Street officials were exploring options for currency.
The widespread consultation over the next two months will see around 50 events held around the country including 13 in major shopping centres as well as discussion events with regional chambers of commerce and retailers. A final decision will be announced in December this year.
Charlie Bean, deputy governor of the Bank, said: "Polymer banknotes are cleaner, more secure and more durable than paper notes. They are also cheaper and more environmentally friendly.
"However, the Bank of England would print notes on polymer only if we were persuaded that the public would continue to have confidence in, and be comfortable with, our notes."
Polymer bank notes are made from a transparent plastic film, coated with an ink layer which enables them to carry printed design features. The Bank said they can also incorporate raised print.
More than 20 countries currently issue polymer bank notes, including Australia, which began printing them in 1988, as well as New Zealand, Mexico and Singapore.
The Bank said that, as they are resistant to dirt and moisture, they stay cleaner for longer than paper banknotes.
Tests also show that, unlike paper notes, they would suffer little effect from going through a washing machine cycle, although they can be damaged by ironing.
The Bank also said polymer can incorporate better security features than paper notes and that they are much more slow, expensive and complicated to counterfeit.
Another benefit of polymer currency is that it lasts at least 2.5 times longer than paper so will take much longer to become tatty.
While more expensive to produce, its durability mean fewer notes should need to be printed to replace worn ones, so it should prove cheaper in the long run - possibly saving more than £100 million over 10 years.
Polymer notes' longer-lasting nature also means they are more environmentally friendly. They could be recycled by creating energy from waste in specially-designed plants, turned into bio-diesel, or even made into plant pots or garden furniture.
The Bank said thin, flexible polymer notes fit into wallets and purses as easily as those made from paper.
They are expected to be easier to use for cash-accepting technology, which is often designed for international currencies that typically have smaller notes.
The polymer £5 will measure 125mm by 65mm, and subsequent denomination sizes will be fixed at 7mm longer and 4mm higher, making the £10 note 132mm by 69mm.
Last year there were 2.9 billion notes in circulation with a face value exceeding £52 billion, according to Bank of England figures.
The Bank began issuing handwritten notes shortly after it was established in 1694. The first fully-printed notes appeared in 1853.