When it comes to the issue of using tallow, Lynne Elliot, the CEO of The Vegetarian Society, said it wasn't necessarily an issue for those who follow a vegan/vegetarian diet for their own personal health; however it may be "a massive issue" for those who choose this diet because they are concerned about animal welfare.
"I think that's really just because people take a lot of care and effort to try and avoid using products that are from animal slaughter, in their life," Lynne Elliot, The Vegetarian Society's CEO, told CNBC over the phone.
"So they're very careful about what cosmetics, cleanings products, clothing they use and they've got choices about all those things."
"But this is going to be very difficult for people to avoid using the currency of the land."
Elliot added that the Bank of England had been very supportive of the situation, after the society spoke with the central bank on Tuesday night.
"(The Bank of England) are taking this issue really seriously. They are listening. They are understanding that it's really concerning some people. They've set off to do a full investigation now," Elliot said.
The next two banknotes set to enter circulation soon are both—at present—expected to be made out of polymer: the polymer Jane Austen £10 banknote due in 2017, and the J.M.W. Turner £20 banknote, due out by 2020.
"I'm really, really hoping we might be able to find an alternative going forward," Elliot added.
Follow CNBC International on Twitter and Facebook.