If you want to do this on future broadcasts, there is an app available called My Pod at https://mypodapp.com/

You link the app to Alexa via their website when setting up. Once all set up you can say "Alexa, ask My Pod to play Radio Caroline North".

The bad news is that the free version is heavily stripped down only allowing 5 links, recently reduced from 10. You can create one free playlist which contains up to 5 streams.

Also sometimes it can be flaky at connecting the stream often timing out. You can just say "Alexa, resume" to try again. When it works, it's great and very convenient for including a few obscure streams not included on the big portals.
I hope to find something better but this will have to do for now.