Hi:
I cannot find that model number on the support site.
Enter the product number in this site which is HP's e-partner in the UK.
http://www.best2serve.com/page/rcd_search
Alternatively, if you can read all 25 characters of the W7 product key on your PC's case...
This site claims to have genuine, unadulterated W7 ISO files for download.
https://www.heidoc.net/joomla/technology-science/microsoft/67-microsoft-windows-iso-download-tool
Click on the link labeled Windows ISO Downloader.exe
You can use either the:
Win 7 Home Premium/Pro (as applicable) SP1 or the (Retail version, but the OEM key on your PC's case will work with it)
Win 7 Home Premium/Pro (as applicable) SP1 COEM (This version would be for what HP would have used--System Builder)
N is for European Union (EU) countries.
K is for South Korean markets.
You can use this tool to transfer the ISO file to a 4 GB USB flash drive or DVD.
https://www.microsoft.com/en-us/download/windows-usb-dvd-download-tool