The housing design was based on an existing model that I found on ThingiVerse: https://www.thingiverse.com/thing:1880449

Using a lot of photos of the original I modified this design considerably to get is closer to the original, and to make it easier to print. My final design can be found on :

https://www.prusaprinters.org/prints/29047-sinclair-zx80-replica

First part : the top cover. 

It took 27.3 hours to print, but turned out really nice. Unfortunately  there was some warping on the edges, but not too bad and I can probably correct this by heating it a little. And 4 solid layers for the top was not enough to completely hide the support structure, so the honeycomb pattern is still vaguely visible on the surface.

Part two : the bottom section.

Since I could not print the whole bottom section on my printer I had to split it into two parts. By adding some support and making some minor changes to the basic shapes, I ended up with two printable pieces that can be bolted and glued together.