Instead of copying and pasting the object try using the Place command under the File menu in InDesign. You will see a tiny icon of the object as part of your cursor when you do. Then click anywhere on the screen and the entire object will be seen onscreen. If there is still a cut off at the top click on the object with the black arrow selection tool and see if you can open the frame on top to see more of the object. To see the object as clearly as it appeared in Illustrator make sure that High Quality Display is chosen under View>Display Performance. Remember, the object is now linked to the Illustrator file and must have the Illustrator file packaged with it for any export or sending to a vendor.
Ah Bill, you got it. Thank you so much.
For anyone reading this with the same problem here's what I did:
- In Illustrator save the logo with the 'PDF compatible file' ticked

- In InDesign choose 'File - Place' (it went into InDesign a bit big so i chose Object - Transform - Scale to make it smaller).

This worked for me. I think my error was that I was copy pasting the logo directly from Illustrator into InDesign. As my settings were already good I knew it wasn't them.
ADMIN: Can you mark this as ANSWERED please, I can't do it as the forum doesn't recognise me as the OP becuase it changes my username every time I login.
Thanks massively to everyone for their help xx