When doing hanging leg raises, I get cramps in my thighs after very few repetitions, usually after about 5 or so. This stops me progressing in the training. What causes them and what can I do to progress past this point?
I would make sure you're doing these:
Warmup. I don't do anything until I've broken a sweat and have exercised the particular parts of my body I'm about to use. Running doesn't warm you up for bench pressing, and pushups don't warm you up for squats. It's rare for me to warmup for more than 5 minutes, alternating between Turkish getups, jump rope, and overhead squatting an empty bar. Rowing machines work good too, but I like using weights to warmup if I'm lifting.
Electrolytes. The biggest problem I ever had in this department was in the tropics where the heat and humidity caused incredible sweating. I had to drink a cup mixed with ~1/4 tsp salt before I worked out to get through it.
Personally I'd avoid targeted movements like that unless you're trying to solve a problem. The more typical-human-movement compound stuff tends to keep you in balance without having to think about it much.