It would be the first time in the 300-year history of official UK banknotes that they would be made of a material other than paper.
The bank also intends to make the new banknotes around 15% smaller than the current versions.
"Polymer banknotes are cleaner, more secure and durable than paper notes," the bank's deputy governor Charlie Bean said.
"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."
The consultation itself will last until November and the decision on whether to introduce them will be made in December.
Polymer notes have been in use in Australia for 25 years, and were recently been introduced in Canada, under the governorship of Mark Carney.
The Bank of England said it had been researching polymer banknotes for three years, but the final decision to launch the consultation was made by Mr Carney, who is now Bank of England Governor.
What polymer banknotes would look like
Polymer notes would potentially be introduced for the new £5 note, which will feature Winston Churchill, and the new £10, which will feature Jane Austen, in 2016 and 2017 respectively.
Although the polymer notes cost around 50% more to produce than existing paper notes ("a few pence each" according to chief cashier Chris Salmon) they also last longer - between two-and-a-half and six times.
Current £5 notes have a life of around two years.
The bank said it hoped the new notes, which are harder to counterfeit, would reduce banknote forgery in the UK, which is at higher levels than many other countries.
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