YouTube/Vimeo embeds breaking layout

I'm struggling with the standard WordPress video embed code (ie. just copying the URL into place or wrapping in [embed][/embed]). As the screen width reduces the text below the video gets lost behind the video.

I found this post – https://premium.wpmudev.org/forums/topic/youtube-video-not-being-contained-by-element-and-breaking-mobile-view – and tried implementing these bits but no joy.

Any one got any ideas?

http://markmeynell.net.s218979.gridserver.com/2015/10/01/q-marks-the-spot-treasure-map-85-october-2015/

(This is an old site I'm working on resurrecting)