The way we do it, is using the Email Manager, so if the customer fills in a form a on the website, this when submitted generates an email that is sent to a dedicated inbox. 

CRM can be told to monitor it picks up any emails and using a script is told what to do with it. (e.g. create a new case against the company / person where an email address is recognised and populate fields based on what is in the email)

The way we do it, is using the Email Manager, so if the customer fills in a form a on the website, this when submitted generates an email that is sent to a dedicated inbox. 

CRM can be told to monitor it picks up any emails and using a script is told what to do with it. (e.g. create a new case against the company / person where an email address is recognised and populate fields based on what is in the email)

We are currently doing the same but the problem comes in when the email is received from the Website, it is not linked to the email address captured from the website by the client but rather the email address of the Website Contact Us form sender. 

This makes it difficult with auto-reply assigning a case number for the customer's reference

I was looking at feeding CRM directly with the necessary fields populated from the Contact us form on our website 

Sounds like the script used to handle the email needs adjusting, if you're capturing the person's email then you should be able to edit the script to use that as the reply address