Is the new Apple Cassical App included in Apple One (UK) subscription?

Yes based on -> Apple Music Classical -> Apple Music Classical – Apple Support (UK)

• And if you have an individual, student or family subscription to Apple Music, Apple Music Classical is included with your subscription. 

Read also the Frequently asked questions

See also -> https://learn.applemusic.apple/apple-music-classical

You have Apple One, so you also have Apple Music, see -> Bundle Apple subscriptions with Apple One

Bundle Apple subscriptions with Apple One - Apple Support

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Apple Music, Apple TV+, Apple Arcade, iCloud+, and more are bundled into one simple plan with Apple One. With a Family plan or Premier plan, you can share it all with your family.

I need to call support.

Get more help and assistant from Apple directly, see Contact Apple for support and service -> Contact Apple for support and service – Apple Support (UK)