Is there a way of making a chat page similar to WhatsApp to integrate into the website or is there a hopefully free way of including something similar? Or is it blindingly obvious how to do it and I have missed it?
There's no "live chat" type app as part of Voice itself, though since you can embed code onto a page, if you can find a third party app that does what you want you can probably get it working on a page of your site reasonably easily.
The first thing to do though would be to think about exactly what it was you wanted - what purpose it would have on the site? who is the audience for the chat? how would you control who could chat (and prevent spam/abuse/etc)? how would it be better than just using WhatsApp? would it be for people to chat to you for help or for people to chat to each other? etc.
Then once you have your requirements, see if there's an embeddable third party tool that would do it (which is also hopefully free or has a free tier in their pricing structure), create a page on your site, and embed it.