New iMac 27" Shuts down several times a day.

I'm a little reluctant to start paying money to find out what's happening with a brand new £2000 iMac

The basic version of Etrecheck is free and will work for what we need here. EtreCheck will save you suffering a protracted game of "20 Questions" about your hardware and software load as we try to work through your issues.

Are you running Google apps? That "watchdog" thing could be a Google issue:

https://www.zdnet.com/article/google-releases-enterprise-malware-watchdog-for-mac-os/

There are also some suggestions that this is due to external monitors and an update to the latest Catalina supplemental release may fix it.

Without knowing what, if any, external devices you may have or what software you may be running it's difficult to offer an opinion. If you'd run and post an etrecheck report perhaps that would give us some pertinent information https://www.etrecheck.com/

To post the entire report follow the instructions in Old Toads user tip on the add text feature How to use the Add Text Feature When Post… - Apple Community

Download and run Etrecheck. Get the free version. Etrecheck is a diagnostic tool that was developed by one of the most respected users here in the ASC and recommended by Apple Support  to provide a snapshot of the system and help identify the more obvious culprits that can adversely affect a Mac's performance.

Copy the report

and use the Add Text button to include the report in your reply. How to use the Add Text Feature When Posting Large Amounts of Text, i.e. an Etrecheck Report

IMPORTANT:

Before running Etrecheck assign Full Disk Access to Etrecheck in the Etrecheck's Privacy preference pane so that it can get additional information from the Console and log files for the report:

Also click and read the About info to further permit full disk access.

Then we can examine the report and see if we can determine what might be causing the problem.