Having been on a low carb diet myself for ages (first to lose weight and now to maintain weight loss and for my health) I can sympathise with your problem. I used to get constipated at first too - I think it's just while your body gets used to the change in diet. My solution was to take a couple of senokot tablets, once a week for a while. This got me going and, over time, the problem solved itself. You could also try adding bran to meals or three tablespoons of linseeds per day (this is cheapest bought from Tesco's NOT health food shops!). Stick with the diet and the problem will resolve - and you'll lose weight! Just make sure you're eating enough fat - lots of protein with too little fat can make you unwell.