I’ve got it… for anyone else having this problem…
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Go to where your media is kept on your WordPress.com account i.e. Media > Library
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Go to edit the video and make sure that ‘Display share menu and allow viewers to embed or download this video’ – this is so that you can click the ‘share’ menu on the embedded video on an actual page, grab the embed link and paste it into your html code
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Go back to your media page and disable the share menu again if you want to protect your videos.