Where on my MacBook can I find Downloaded BBC Podcasts.

~/Library/Group Containers/243LU875E5.groups.com.apple.podcasts/Library/Cache

They're not named - just random characters, so you'll have to work through them to find the BBC ones you want

The ~ means your user name - in Finder click Macintosh HD in the LH pane then Users, then your user name and that's where Library is, so you should be able to navigate from there. Alternatively just go to Finder and in the menu bar Go/Go To Folder and paste the whole lot into the box that pops up.

I'm also on 15.2, so it will be there somewhere. If, for some reason yours has a different reference number then go to the Containers folder and find the groups.com.apple.podcasts folder.

Save or download episodes in Podcasts on Mac - Apple Support (IE)

You're welcome. I never understood why they made Podcasts such a complicated unhelpful app. Never been the same since iTunes.