Both my Internal and external URL point to https://remote.mydomain.co.uk/owa/EWS/Exchange.asmx

I think this should be https://remote.mydomain.co.uk/EWS/Exchange.asmx

I also found that Basic authentication is NOT set.

Would this fix it ?

Set-WebServicesVirtualDirectory -Identity Contoso\EWS(Default Web Site)-ExternalUrl https://www.contoso.com/EWS/exchange.asmx -BasicAuthentication $true -InternalUrl https://contoso.internal.com/EWS/exchange.asmx
(is there any possibility of ANYTHING that's currently working being effected by the above Command?) 

Hi

You can also login to the EMC (webpage) and set it from the server settings.

The external URL is right, but the internal one depends on your current configuration. Do you have split DNS, legacy Exchange servers etc?

Here is a snapshot of the authentication methods:

"is there any possibility of ANYTHING that's currently working being effected by the above Command?"

All you clients that are currently using EWS, like:

• Entourage with EWS extension
• Outlook 2011
• Apple Mail
• BlackBerry Servers: Mozilla/4.0+
• Microsoft OCS 2007 R2: OC/3.5.*.*
• Microsoft Lync 2010: OC/4.*.*.*
• Microsoft Lync Web App: CWA/4.*.*.*
• Microsoft Lync Phone Edition: OCPhone/4.*.*.*
  

The external URL is right, but the internal one depends on your current configuration. Do you have split DNS, legacy Exchange servers etc?

Here is a snapshot of the authentication methods:

"is there any possibility of ANYTHING that's currently working being effected by the above Command?"

All you clients that are currently using EWS, like:

• Entourage with EWS extension
• Outlook 2011
• Apple Mail
• BlackBerry Servers: Mozilla/4.0+
• Microsoft OCS 2007 R2: OC/3.5.*.*
• Microsoft Lync 2010: OC/4.*.*.*
• Microsoft Lync Web App: CWA/4.*.*.*
• Microsoft Lync Phone Edition: OCPhone/4.*.*.*
  

None of the above is used - only Outlook 2007, Outlook 2010 and Outlook 2013

Webaccess, iPhones, Android Phones via Activesync

The reason for asking is do I risk the chance Breaking existing functionality... (company is very busy at the moment & can't risk breaking anything)

I was thinking of changing the URL via ECP (I think that is where it was first setup!)
I guess a REBOOT will be necessary....

if still not working - I can change it back!

NB: I used the procedure of setting Internal & External URL the same as per deployment assistant

http://technet.microsoft.com/en-US/exdeploy2013/Checklist?state=2284-W-DwBEIgAAQAAgAAEAAQAAAA~~