If a customer cancels their own online booking, is their Stripe payment refunded automatically?

No. Self-service cancellation changes the reservation's status — it does not touch the payment. If a card was charged, that charge stays exactly as it was; BRM does not contact Stripe at all as part of a customer cancelling their own booking.

What actually happens: the reservation moves to Cancelled and every price field on it is zeroed — total, tax, extras, delivery. Because the payment record is untouched but the price is now £0 / €0 / $0, the reservation will look overpaid in your reservations list. That's your signal to look at it, not a system alert — nothing flags the booking or notifies anyone that a refund might be owed.

Where self-service cancellation comes from

Customers can only cancel their own booking if your store has Settings → Features & customisation → Self Service Cancellations switched on. When it's on, a cancellation link goes out with the reservation's confirmation/invoice (email and/or QR code, depending on your notification settings) and stays live up to a configurable cut-off — 12 hours before the booking starts by default. Inside that window, the customer clicks through and the booking cancels immediately; no operator approval step.

You can turn on separate notifications (Settings → Notifications) so you and/or the customer get an email when a self-service cancellation happens — that's the closest thing to a heads-up, and it's worth switching on if you offer self-service cancellation at all, precisely because nothing else will tell you a refund might be due.

If you do want to refund it

There's no automatic or one-click path from a self-service cancellation to a Stripe refund. You'll need to process it the same way as any other refund: Back Office → the reservation's payment → Refund. See refunding on Stripe (within BRM) for the full walkthrough.

Because the cancelled reservation shows £0 owed, it's easy to read it as "settled" and miss that money is still sitting captured against it — worth a periodic check of recently self-service-cancelled bookings if you offer this feature.