Hello F Younghusband,
welcome to the Pages Discussions. The only reason for the white space I can imagine, is the extra Layou-Border after a layout area. Look inside the infopalettes "Layout" section. At the bottom, there are four number fields where you can insert extra borders for every layout you inserts into the document. Look, if there is a setting for the field "After". Set it to "0".
But after reading your post, I think you have inserted the layout break unintentionally. So you can delete the white space, too, if you delete the layout break by placing the text cursor behind the last word of the page, where the space is, and press the delete key. But then the space is behind the last word of the fomerly second layout area.
I hope this was a clear description 🙂
Frank