That's edge enhancement over-sharpening the image. I'd double check in the picture settings that you have any edge enhancement disabled the next time you use it (it's usually best to disable anything that adds edge enhancement to any source). As others have suggested, it's entirely possible that it's in the original broadcast image itself however, as edge enhancement may have been applied by the BBC to try and sharpen lower quality material or iPlayer itself may automatically apply the effect on lower quality streams.
I rarely use iPlayer much but when I do it's usually from a connected laptop or console to my TV. The picture quality of regular SDR material always looks very soft even at the highest quality streaming playback across all devices due to how compressed the material on there tends to be. It's the type of picture where any edge enhancement being applied will scream out at most eyes, looking worse the larger the screen size and your closeness to it.