How can i test hyperlinks on a web page using Test Complete

It's not a simple web page with hyperlinks on it.

Such as: https://www.google.co.uk/

... which will appear as a hyper link in my reply.

That would be simple to test. (In fact, try it. Object spy it with TestComplete. Record yourself clicking it and play it back. It should work just fine)

What you have is an embedded document of some sort (a PDF is a fair guess) and it has link embedded within it. PDF's are not the most automation friendly type of document. But whatever type it is (we don't know this because we don't have the page in front of us to inspect), it is obviously obscuring the links to you. But you should be able to extract the link from the PDF or something. Probably. There are a couple of add-on's you can use for TestComplete which make PDF handling a little easier, but I've never used them personally, I'll leave others to comment there.

So you need to figure out two things:

1. What type of embedded document it is, followed by ...

2. How you extract text/links for that document type.