Through some trial and error I found the solution.
It’s far simpler than I thought.
For example, because my page is the homepage, I use this as my link in the menu:
/#one
As opposed to:
#one
And it works. It doesn’t matter what page I am on, once I click that link it takes me to the correct page and then to the correct section.
If you want to target the section of another page, just do the following:
/?page_id=21#four
Of course, this doesn’t let you have the flexibility of selecting the page name in the menu customisation page, so you have to know the pages ID for this to work.