The images looked fine whilst I was editing the page, but when previewed they appeared rotated.
Searching online showed this to be a known problem, all to do with EXIF data. You can read more about EXIF data by following this link to How-To Geek
The Wordpress problem seems to be that the images are recorded with one orientation and then displayed with the rotation stored in the EXIF data added to them.
The easiest way I've found to get the images displaying properly is to first strip the EXIF data and then to rotate them appropriately before uploading. There are instructions on the How-To Geek link above on how to strip EXIF data in Windows.
It's a lot simpler in Ubuntu or similar.
First, install exiftool
sudo aptitude install exiftool
Exiftool allows you to look at the EXIF data in an image as follows
We want the data stripped. Copy your images to a directory (I just copy them to my pristine desktop) and then run the following command
me@comp:~/Desktop$ exiftool -all= -overwrite_original -ext jpg .
And that's it. Time for a cup of tea.