Is it illegal to not have a cookie banner?

No. The absence of a cookie banner is not illegal by itself.

Privacy rules generally require websites to obtain valid consent when consent-dependent technologies are used; they do not prescribe one mandatory banner design. Consent may be requested through a banner, pop-up, message box, or another suitable interface. The ICO expressly recognizes different types of consent mechanisms. ICO guidance on cookie consent mechanisms

The violation is therefore not “having no banner,” but using technologies that require consent without meeting the applicable consent requirements.