When you play a programme, BBC Sounds will automatically play the next episode when you get to the end of an episode. If there is no next episode we’ll play something that's related to what you're listening to, for example, something from the same category. We call this autoplay.
On the BBC Sounds website
You’ll notice that a ten second timer will appear just before the programme you’re listening to finishes. You can click on the image for the next piece of content to skip the timer.

- How do I turn off autoplay?
You can disable autoplay by selecting the black and orange toggle switch labelled Autoplay, which is located at the right of the 'Coming up next' section.
To turn autoplay back on again, select the same toggle switch.

On the BBC Sounds app
Autoplay will be switched on by default on the BBC Sounds app. Just start playing an on-demand programme, then tap on the queue icon at the bottom right corner to see what will play automatically after that episode has ended. 
- How do I turn off autoplay?
Just go to My Sounds > Settings and toggle off the Autoplay option.