Hi Andy,
Thank you for posting your query in Microsoft Community and giving us an opportunity to assist you.
From the issue description, you are facing issues with installing .Net Framework 3.5 and receiving error code 0x800F081F.
There is a Microsoft Knowledge Base article that provides methods to troubleshoot this issue. I would suggest that you visit the link and use the methods to resolve the issue.
Error codes when you try to install the .NET Framework 3.5 in Windows 8 or in Windows Server 2012
http://support.microsoft.com/kb/2734782
You may also refer this link for more information:
Installing the .NET Framework 3.5 on Windows 8
http://msdn.microsoft.com/en-us/library/hh506443.aspx
Hope this information helps. Let us know if you need any further assistance related to Windows.