AH!
Blender has changed since the lecture.
In the 86. ‘your first texture’ lecture. Mikey, in the Materials tab, clicks the button beside the colour swatch to the right.
NOW in 2.91 I am using, The button to click is on the left of the swatch. That brings up the ability to load an image as the texture.
It actually makes sense when you get further and use nodes, as the image texture node plugs into the Principled BSSF which is represented in the materials tab, at that same point. It confuses a lot of experienced users as they probable never use this route to add nodes, preferening the full node ‘shading’ workspace.
Red arrow pointing out the place to click.