Hi. I’ve just taken out the Apple one for £14.95 per month. I already had Apple Music and Apple TV that I was paying for separately. Will this automatically stop now? Also will I get any refund for money I’ve already paid for these services?

See the following from Bundle Apple subscriptions with Apple One - Apple Support

If you already subscribe to Apple Music, Apple News+, Apple Arcade, or Apple TV+, you don't need to cancel those subscriptions. They will automatically be canceled when you're billed for Apple One.

and

Apple One includes a free 1-month trial for services that you don’t already have. After your free trial, services that you previously subscribed to are automatically included in Apple One. If you recently canceled a service, you might not be eligible for the free trial. Your plan automatically renews after the trial.

I believe you will get a refund (may take days), but I have not done that myself.