The cause of the entire instance is non-communication and assumption. Theory of communication teaches us never assume anything and communicate well in advance. When these principles of communication are not followed, it leads interpretations that suit to the respective party. This disagreement could balloon into the conflict too.
Your one of the terms of appointment mentioned in the appointment letter say that "You would deemed to be the confirmed employee of the organisation only when a communication in writing confirming your services is issued." It is explicitly worded. Therefore, non-communication from the HR department cannot imply as confirmation of the employment.
Partially, there is non-communication from your side also. Nothing wrong in looking for better opportunity as such. However, you could have told to your future employer that you will confirm exact date of joining after conformation from the current employer. You assumed and interpreted the situation the way you wanted. Hence this disagreement.
As a solution to your problem, you may write the application to the MD of the company and tell him that the deduction of one month salary is wrongful and against the clause mentioned in the appointment letter. If he does not respond or responds unfavourably, then you may approach the Labour Officer (LO) of your area and tell your problem. If he intervenes, the better. But if he does not then litigation is only the solution for you.
Before approaching LO, I recommend you obtaining your experience-cum-employment letter. Ensure that there are no outstanding dues against you. You may keep HR Department of the current employer posted, if you approach LO.
Final comments: - Going contrary to the terms of appointment, speaks poorly of HR department. It is the duty of HR department to bring clarity through proper communication on the status of the employee whether he is confirmed on still on probation. On the contrary, interpreting non-communication that suits to their advantage is unprofessional. This is the classic case of the importance of the organisational communication. When organisational communication fails, it erodes the credibility of the organisation in general and of the HR department in particular. In almost in his entire career, the originator of this post could look at HR suspiciously.
13th February 2017 From India, Bangalore