But should you be rushing to get rid of all your paper notes before the deadline, or could some of them have some value for collectors?
In most cases, the answer is no, says Thomasina Smith, a banknote specialist at auction house Spink & Son.
Unless you're prepared to wait a while, that is.
"A lot of people still have them – they're generally not really worth more than their face value," she says.
"However, that's not to say that in 20 years' time that people won't be interested, because they will – notes from 20 years ago are valuable."
Exceptions to the rule
There are very occasional exceptions, with some recent paper £10 notes already worth good money. Last summer, an old £10 note featuring Charles Darwin was put up for auction on eBay with a price tag of £1,500.
In this case, the reason for the high asking price was the unusual serial number: EB11 111111.
In other cases, collectors will have an interest in particular notes for reasons that are impossible to predict – because the serial number begins with the person's initials, for example.
Could my old £10 be worth anything?
In short, they'll need to have something a bit special about them to be worth any more than their face value.
For example, runs of notes with consecutive numbers in perfect condition can be worth quite a bit extra.
And errors will always bump up the price of a banknote.
"We see errors now and again. Some are printing errors, for example where the paper has creased and you're missing some ink," says Smith.
"In other cases, it's a processing error, like the note being smudged or something having got onto it during the printing."
Some old paper £10 notes, like the one that sold last year, may be worth more than their face value because of their date of printing – as long as they're still in perfect nick.
"What collectors really look for is the condition of the note, and their scarcity," says Smith.
"What they want is first runs, last runs and interesting serial numbers. First runs are pretty obvious because of the prefix."
With the old paper £10 note still in circulation, though, the serial numbers for the last run are still a complete mystery.
"The Bank never gives out this information, so it's up to the enthusiast to find out for themselves," says Smith.
"They probably have an idea; some people can guess. For example, with the £20 note, they think the latest is JH80. For the old £10 note, the last run is something no-one knows yet; they're all still trying to find out."
Rumour has it that collectors are expecting the serial number of the last run to begin with 'ME40', or thereabouts. It can't be anything lower, but it may be worth keeping any with this prefix – definitely anything beginning 'ME' but with a higher number.
And if the gamble doesn't pay off, there's always the chance to make a profit at some time in the future. You never know, you might find that your grandchildren thank you one day.