Is it accurate to say that only £10, £20, £50, and £100 banknotes are permitted in the UK?

The UK's banknotes are actually quite diverse, and it's easy to forget all the denominations. While £10, £20, and £50 notes are commonly used, and the £100 note exists, it's not the whole story. The key here is the humble £5 note. Introduced in its current polymer form in 2016 featuring Winston Churchill, it's a staple of everyday transactions. Before that, it featured Elizabeth Fry, a social reformer. The Bank of England is responsible for printing these notes, and they're legal tender throughout the UK. So, the statement is false because it omits the £5 note, which is a valid and circulating form of currency. It's a good reminder to be aware of all the different types of currency in circulation.
In the land of the Queen, you can also find £5 notes.