I have a program working in the Android Emulator. Every now and again I have been creating a signed .apk and exporting it to my HTC Desire to test. It has all been fine.
My problem was: I used the Debug Apk, that was generated while I did the Run command from Android Studio
Solution was: Instead of using this file, clean project and click Build > Build APK(s) from Android Studio. Then you can use the generated APK from the usual folder (app/build/outputs/apk/debug/)
The file that was generated like this installed without a problem.