You and the buyer will only get these codes if you are both app users, it doesn't matter if you don't have them though, you can still mark the items as paid and dispatched - you will need to use a desktop browser to do this.
To mark as Paid and Dispatched. In the Seller Hub, open the Awaiting Payment orders, here:
https://www.ebay.co.uk/sh/ord/?filter=status:AWAITING_PAYMENT
and then click the box on the left of the item. Then you should see a drop down menu, above the listings, with the title "More" and one of the options in that drop down menu, is Mark as Payment Received and you should also be able to Mark as Dispatched.
