With the Windows 10 Creators Update Microsoft introduced a new feature than enabled you to resume Microsoft Edge tabs when you switched devices.
With the Creators Update the feature only worked if you were in the US English region, but it seems with the latest Windows Insider build (16179) the feature is available for UK systems.
Update: It seems Microsoft switched this on via a backend service as it is now working on machines with the Creators Update.
The resume feature uses Cortana to sync the devices. Opening up Action Center shows Microsoft Edge tabs from other devices, click on the page title and it will open up a new tab in Microsoft Edge.
The feature only shows up on the new Redstone 3 builds (I noticed it on build 16179) but it does pickup open tabs from machines running the Creators Update.