Assuming you are no longer serving, if they have genuinely overpaid you, regardless of the fact that it may be due to their ineptitude, you will have to repay the money.
If you don't repay the money, you could face legal action (civil action) with the potential of winding up with a County Court Judgement against you. I don't know your personal circumstances and this may not apply but generally speaking, say goodbye to a mortgage, new car or any other credit agreement for 6 years from date of CCJ.
The worst thing you can possibly do is to ignore them.
Argue the toss by all means but make sure you do it in writing, with proof of posting (Special Delivery is always the best). Tell them you disagree and would like clarification - they will probably send you a thorough explanation. My dealings with MOD departments have always been very positive, in that you do get an answer and usually a very full answer - don't expect the same in civvy street.
If it turns out that you do owe the money you may also be able to negotiate repayment terms - could become an interest free loan.