How to get girls more interested in computer science?
If you're just looking for the key points on how you can begin to solve the problem, you need only read the second section, but the first section provides valuable context on what the actual problem is and the root causes.

Why are so few girls interested in Computer Science?

There is an issue, not limited to CS, but throughout STEM fields (particularly Physics, Mathematics and Computer Science, according to recent examination statistics) with gender balance, where women are extremely underrepresented. In 2014, only about 10% of entrants for the Computing A-Level were female. 

Miura (1987) suggests that women's self-efficacy regarding computing is lower, which leads to lower interest in the field and lower uptake at undergraduate level.

Fisher, Margolis &amp; Miller (1997) also propose that women have less previous experience than men in the field—many have already started to self-teach or practice at home, whereas this is less true for women in the study. They also state that, from their interviews, women seemed to appreciate computing more as they went through their studies, whereas many of the men in the study showed a keen interest as soon as they were introduced to computing.

Fisher &amp; Margolis (2002) discuss the "Geek Mythology"—the stereotypical male computer scientist—and its effect on women:


  While the stereotype of the computer science student as someone who is
  myopically focused on computing is rejected by many male and female students,
  women report more distress and are more affected by the perceived
  difference between themselves and their peers. One-third of the male students
  we’ve interviewed say they differ from the stereotype, that they have
  a broader range of interests than just computing. But twice as many women
  (more than two-thirds of those we interviewed) feel different from the
  stereotype. And 20 percent of the women we interviewed question whether
  they belong in computer science because they feel they do not share the
  same intensity in focus and interest that they see in their male peers.


How can this be changed?

Benbow &amp; Vivyan point to a pedagogical solution which may benefit:


  Pedagogical interactions are an important factor in determining
  whether students feel included or excluded in a particular educational field, and our findings in
  this regard confirm results from previous studies. Most significantly, students across our sample
  reported that working with real-world problems, as well as active instructor encouragement in light of student
  questions and peer collaboration, made them
  feel more comfortable and more confident as computer science majors—often despite
  brogammer-oriented field norms. 


There are many groups aiming to change the culture around computing, such as Django Girls, an organisiation running free, one-day courses for girls and women interested in web development with HTML, CSS and Python. Events like this would seem to satisfy the goals of a supporting group of instructors, and a real-world problem to solve, which favours participation from women.

As a teacher, even changing the classroom environment may help to favour women and girls. Cheryan, Davies, Plaut &amp; Steele (2009) state:


  People can make decisions to join a group based solely on exposure to that group’s physical environment.
  Four studies demonstrate that the gender difference in interest in computer science is influenced by
  exposure to environments associated with computer scientists. In Study 1, simply changing the objects
  in a computer science classroom from those considered stereotypical of computer science (e.g., Star Trek
  poster, video games) to objects not considered stereotypical of computer science (e.g., nature poster,
  phone books) was sufficient to boost female undergraduates’ interest in computer science to the level of
  their male peers. 


The solution to this problem might not be one big change; rather, lots of little changes might improve participation from girls and women in CS classes.

Trying to create real-world scenarios, in a balanced classroom environment may bring some more success, but it's often hard to know if the solutions you try actually have any effect. Ensuring the culture of the class doesn't become too male-oriented might also help to avoid bias against women in the demographics.

I'd be very interested to hear anyone's experiences with applying methods like this, and whether they did seem to make a perceptible difference.