How to set a 'page' as parent of a custom post type?

For various reasons, I would like to use a 'page' in preference to an archive page for one of our custom post types and have this be reflected in the permalink structure. I am struggling to find out exactly how to do this.

What needs to be achieved is a permalink structure that, when viewing a custom post, show as: mysite.com/[page-name]/[custom-post-type-single]

I'd be extremely grateful for any help that can be offered.

NB I have tried the Post Type Parents plugin but it does not work for me.

This tutorial is close but it requires you to set the parent page id for each post individually. My posts will all have exactly the same parent page.

I have ACF Pro, if this can be harnessed to do the job.