The company, which has been printing money for the bank since 2003, is expected to sign a contract in October that will install it as the printer of the nation's money for almost 10 years.
Plastic banknotes are due to debut in the UK in 2016, starting with the new £5 note featuring Winston Churchill, followed by the Jane Austen £10 note a year later.
De La Rue, which has been printing banknotes since 1860, moved into polymer notes in 2012, but lost out in a bid to provide the polymer to the Bank earlier this year to the Cumbria-based Innovia. In a statement on Monday, the Bank said De La Rue was its preferred bidder, meaning it will print the first British plastic notes on Innovia-provided polymer at a secure printing works in Debden, Essex.
Shares in De La Rue, which prints more than 150 national currencies, as well as passports and identity cards in more than 65 countries, jumped 3.6% to 769 pence following the announcement.
The UK is following in the footsteps of Bank of England governor Mark Carney's native Canada by opting for polymer notes. The bank expects to save £100m a year and has sought to quell environmental concerns about the use of plastic, by saying that the notes will last two and half times longer than the current paper-cotton notes.
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