Can I stop the annoying Allow Access button when emailing via Outlook

This can be resolved through Outlook's Trust Center

Trust Center Settings

Since Outlook 2007, no security prompts will be shown when you have a virus scanner installed which reports its status to Windows and reports its status as “Valid”.

Outlook 2007

Tools-> Trust Center…-> Programmatic Access

Outlook 2010 and later

File-> Options-> Trust Center-> Trust Center Settings…-> Programmatic Access

In this configuration, you shouldn’t get any security prompts. The greyed out settings can only be changed when you start Outlook with administrative privileges.

The greyed out settings above determine whether or not a prompt is being shown. The default setting is: Warn me about suspicious activity when my antivirus software is inactive or out-of-date (recommended)

This means that a security prompt is only triggered when your antivirus status is reported as “Invalid”. The other 2 options either always show or never show security prompts regardless of the antivirus status.

As the settings are greyed out, you can only change them when you start Outlook with administrator privileges. You can do this from the context menu that you get when you hold the SHIFT button while right clicking on the Outlook shortcut button in Taskbar while Outlook is closed.