What makes you think 1200kcal/day is the right thing to do? That's probably such a drastically low calorie intake that your metabolism's slowed down to compensate for it. Most people shouldn't be eating any less than about 2,000kcal/day if they're training regularly. Particularly small framed people or people with already low body fat levels may need to go down lower, to about 1,500kcal, but that's about as low as anyone's ever likely to benefit from.
If I were you, I'd start eating more. Don't just start binging, but go up to 1,500kcal on training days, and 2,000-2,500kcal once a week. You might initially gain some weight, but if you're training properly, it'll be the right kind of weight, and it'll help to reset your metabolism.
Training-wise, you should be doing intense resistance training and intense cardio.
I'd recommend doing proper fullbody strength training 2-3x per week, with the honest goal of improving your squats, bench press, deadlift, overhead press, pull ups and rows. If you can't even do all those exercises, then work on being able to do the exercises with good form first, then worry about increasing weight/volume. This is the stuff that spares lean body mass, so that any weight lost is coming from fat.
You should also be doing metabolic resistance training (eg circuit training, Tabata training with resistance exercises), high intensity interval training, or some combination of the two. This is the stuff that shoots your metabolic rate up. There's some conflicting information out there as to how long lasting the effects are...some studies indicate a very short-term increase in metabolic rate, others indicate anywhere between 12 and 36 hours of increased metabolism (by about 10% above normal) after training. Ease into it, and just like strength training, make sure you do everything with good form before you worry about doing it hard and fast to minimise the risk of injury.