Modern British warship survivability relies on subdivision and damage control

Are modern warships built around battleship-style armor zones that resist their own guns?

No. British designs rely much more on subdivision and damage control than on a battleship-style armored immunity zone.

Modern British warships are not designed around armor thick enough to defeat their own guns at selected battle ranges. Their protection philosophy emphasizes subdivision and the ability to contain flooding, fire, and system loss. The design priority is to keep the ship afloat and functional after damage penetrates. This approach differs from the armored immunity zones used in battleship design.