There are a couple of digital banks like Monzo. Atom, Tandem, Starling and more (there's another one for digital nomads, I don't remember their name).

Then there are also other banks like Tesco/Sainsbury's which are definitely not 100 years old. More like started in 90s (but perhaps these reused some old banking licenses from other banks so don't count as "new").

Especially lately there has been a boom in fintech and lots of new challenger banks are appearing and getting banking licenses so that claim is definitely not true today, perhaps it was true a decade or two ago.