Both of the keys need to be well out of range of the car, if the key is within diction range of the car, the boot can still be opened independently of the doors, even if they are still locked.
You should be able to open the boot with out using the fob, if you have it in your pocket.
When you close the boot, it will automatically re-lock after walk away.
Lock the car with the fob and place the keys in the house, then return to the car and try opening the boot by lifting the MG badge.
It should NOT open now !.