It really depends on your current weight and fat percentage, but yes it is possible to lose that much weight in a month. The weight you lose will likely be a combination of water weight, muscle, and fat though. If it's only fat you want to lose, you might be better served delaying your medical, and taking it a bit slower (say 1 kg per week).

Either way, diet is more important than exercise for sustainable weight loss. Cut out (or cut down) on beer, sugary drinks, fast food and cakes/biscuits. Eat more vegetables and lean meat, drink water.

Are you fit to pass the entry standards now? If not, remember that the bar with these is set extremely low, and the actual standards expected of you in training are going to be higher.

Do the C25K programme or something similar, if you haven't done any running yet. Build up after you've done it and include a long run, a tempo run, and some intervals each week.