Hiya, when I was on Atkins I would regularly get these cramps but in my calves. They would wake me up howling! I was told that it's a lack of potassium due to not eating enough on Atkins. Potassium assists in muscle function which is why the cramps occur when we don't get enough. It can also cause fatigue and constipation. Potatoes are really high in potassium as is fruit and other carby stuff we don't eat on a VLCD. A quick google will be able to give you a list of potassium rich foods- most foods do have potassium in but obviously some are higher than others, so it's a case of finding the lowest cal/ carb ones. Chicken, turkey, fish and veg like spinach, broccoli, cauliflower and cucumber all have good potassium levels and are pretty low carb and low calorie.
I would suggest trying a meal such as a piece of chicken on some 'cauliflower rice' (grated or blitzed raw cauliflower and nuked without water in microwave until al dente) with a bit of spinach, and see how that effects your cramps. When I used to have them, a higher potassium meal would work really quickly- I could have the meal for dinner and I'd get a good night's sleep!
Good luck, I hope this helps.