So I have a Gigabit Fibre internet connection, and WiFi showing >300MBits, yet, youtube, on the website, goes to 360p.
if i instead watch the same video on /embed/<videoid> it just works in hd.
@youtube fix your website (you won't, i use edge, you have to slow it down)
Have you tried clearing the browser's cache & cookies to see if that fixes the issue? Here's how: https://goo.gl/e2dYZt . Also, try using a different browser or Incognito mode to check if that makes any difference.