Photo 1 - use a coping saw to cut away all the exposed 45° bits (The end grain, or on MDF the exposed stuff) I used my scroll saw as the length was easy enough to handle
Photo 2 - Different view
Photo 3 – when butted up against the last skriting board it now appears to be a mitred cut.
The advantage is that if the skirting boards aren't exactly vertical the joint doesn't open up. Even if the second skirting board is not vertical the joint still doesn't open up. This technique can also be used for more elaborate skriting boards, just takes a bit more time to cut with the coping saw.