How to install

Go to Edit -> Preferences... -> Add-ons -> Install... then open the addon's .zip file and click the checkbox on the UV Align and Follow addon that shows up. Alternatively you can save the uv_align_and_follow folder into your Blender addons directory.

How to use

With the faces selected in Edit Mode (so that they're visible in the UV Editor), simply select a UV quad so that it's active (white) and select the Align and Follow option from either the UV menu (at the top of the UV editor window), or from the context menu (right-click).

The results depend on the active quad, so its preferable if you use a quad that already resembles what you want the rectangles to look like, but regardless of your choice they'll be laid out in a grid you can easily work with.

There are three follow options (same as with Follow Active Quads), Even will result in similar rectangles, Length Average will account for quad sizes when adjusting (thus areas with larger or smaller quads will result in larger or smaller rectangles) while Length will resize quads independently (which may not be able to be fit into a rectangular grid).