Please have a look at
Note: Where I was used "REST" in above link, in your case it will be "HTTP".
As far as I understand, you need to access a file from an URL provided by the HTML response of your request.
I used to parse some HTML content with Jsoup to extract data or make some assertions.
Once you get the path you cab easily access the file or its content.
By the way could you provide an exemple of your HTML content so we could try to do something ?
You could try some groovy script to access your files if you already know the location.
By browsing the directory, just loop for opening each file and make assertion on the content.
Is that what you're looking for ?