Move some files, with all history, from one project into a new one

["Kerry, Richard" <richard.kerry@atos.net>]

I would like to move some files, from the project in which they have always resided into  a new project.  I would like to keep all their history.
I don't want to waste space by also moving the rest of the old project's history, or historical file contents.

We have a long-standing project, main-system.  A group of files within it are designated as demo-system (sometimes whole folders, sometimes files within folders with other files).
All development is done on the master branch.
It has now transpired that the demo-system files are necessary, but no longer want to be within main-system but in a new project of their own.  So I would like to move them from the main-system repo into a new repo of their own.  I do want all their history but I don't want to take any contents from other files from main-system, which is quite big.
Please can someone advise if there is a particular method I should best use for this.
Do I create a new branch, then delete the rest of main-system leaving only what I want?  Surely if I do that then I would end up with all the main-system file data within the new repo, which would expand its size.
Is there a recommended way to extract certain files with their histories?

Regards,
Richard.