The only way I know to alter this is at the pattern stage, by making the back neckline a tad wider than the front so when sewn it pulls the front and doesn't allow it to gape.
I notice that the dress has darts on the back neckline. Try unpicking them and see if Jo's suggestion works, it may not be enough, but worth a try.
Alternatively or as well try steaming the front neck to shrink it. I often steam shrink on curved seams or facings to avoid little tucks.
Another remedy if you don't want to use elastic, is take the facing off, put 2 or even 3 small darts in the neck. Then make a new facing, cut from a pattern piece that has the darts made up before cutting the fabric. Then apply the facing to the outside of the neck instead of the inside, making a feature of the facing and hiding the darts.
It may not work but worth a try.