The easiest way to access BBC (or other) podcasts is to use the Apple Podcasts App. If not already installed on your iPad, the Apple Podcasts App can be (re)installed from the Apple App Store:
https://apps.apple.com/gb/app/apple-podcasts/id52546302
Information about using the Podcasts App can be found in the [often overlooked] iPad User Guide. Here is direct link to the appropriate section of the Guide:
Find podcasts on iPad - Apple Support
Alternatively, BBC podcasts can be accessed from the BBC Sounds App:
https://apps.apple.com/gb/app/bbc-sounds/id1380676511
Whether you prefer one or other App - or you choose to both - will be largely determined by personal taste and your podcast listening habits and preferences.