I am doing my initial import of existing code into git, it is quite a big codebase so the push is taking it's time.
From what I am aware git gets the changes and then does the upload, so am I safe to continue working while the push is going, or do I need to wait for it to complete before I modify the files?
When Git pushes, it doesn't read or write anything from the working tree, only stuff from the .git folder.
So yes, you're safe to continue working.