Perhaps I should have been clearer in my OP - this is intended to be a replacement for attaching large files in emails.
There are plenty of secure means of moving files without using SFTP.
How do you suggest I train the people the files are being sent on how to use it? Also, for it to work, every person the file is sent to would need their own user account etc.
Anyway, the need of security doesn't necessarily mean that it needs to be bullet proof. In this instance, it's simply a case of not being easily accessible/browsable on a public webserver.
A solution that would work would be say a web app where the user can upload a file, choose how long it is valid for and how many times it can be downloaded. This would then give them a very unique link to download the file, enforcing the parameters set by the uploader.
This would mean that the recipient would just need to click a link to download it. The App can monitor whether the download completed for each client and remove access once the download limit has been set.
Of course this is just an example - I could develop something myself, but I was hoping to save time and find something off the shelf.