Michel Barnier (EU's Brexit negotiator and later PM of France) suggests otherwise.

Exclusive: Former chief Brexit negotiator says staying out of euro and Schengen area would be ‘perfectly possible’" https://www.theguardian.com/politics/2026/jun/18/uk-could-ke...

EEA like Norway would be both a significant improvement, and does not require Euro. I do think we have to get to the point where we can say that actually Schengen was good and we should have been part of it before we get economically overtaken by Poland.