I got rid of that flimsy piece of plastic and tucked the port into the right area, near the heater vent. I chuck out as much plastic as I possibly can

 

I went through this. The OBDII plug is actually pretty hard to seat. I have to take off the trim piece, put it in, then force it to click with a little screwdriver from behind.

So make sure and give it a good looking at before deciding it is broken, it very well could be, but make sure to inspect the little clips on the plug.

 

 

I went the other route and will show a few pics when have time.

Basically, I removed the lower plastic panels (they are black and fugly) from the driver and the passengers sides. Now the underbelly of the dashboard is exposed, but you can't really see the internals unless you bend over and look. Then I took the ODB2 port and attached it to the tube inside the dashboard with a strap. When you need the port, you untie the strap and have an easy access to the connector. Service people at my indie shop like it. By making the port accessible, you prevent further damage.

While I love my Disco, as a professional who deals with human factors and design, I can't stop thinking about how poorly the car is laid out. So many little things in Discos are prone to breaking because they are not designed with humans in mind. From the internal door handles, to the flimsy ODB2 port, to the cup holder in the rear seat, to the controls for the windows. And that's just the beginning of the list. Once I have a garage, I am going to rip out the interior and re-do a lot of things so they would start making sense to humans.

 

Since I'm shipping my Disco in May due to a new job in England, I want to get this fixed ASAP.
I distinctly remember that it is an MOT fail if the OBD port is not secured to the vehicle.