How I almost became the victim of a Credit Card Scam

I had recently got an SBI Credit Card.
On the 23rd, I got  a call from a lady named Khusboo from Delhi from 7836083905 who wanted to verify that the card had reached the proper person. 
She asked my name, Address, DOB, Mother's name, Address,Floor, Nearest Landmark and then my 16 digit Credit Card No. 
I gave her all the details but since I did not have my card with me at that time, I told her sorry, I can't give you that and if she wanted that should phone me the next day. 
She telephoned me on the 24th using the following numbers, 7836082054, 8750180032, 8750031600 as the calls were disconnecting quite often, and again asked me my 16 digit card number. 
I gave it to her. 
Then she asked me for the CVV number on the reverse side. That is when I got suspicious. 
I told her I cannot give her the CVV number. She tried convincing me but I did not budge.
She then asked me to speak to ber boss, one Mr. Rahul who also tried to convice me saying that my card was protected by my PIN and I am supposed to give the CVV for verification.
I told him, no matter what you say, I shall not give the CVV number and disconnected.
I then went to our local SBI branch and informed them.They told me that since I had given them the 16 digit card number, my card was at risk. 
They asked me to go and lodge a GD at the local police station and also to phone the credit card helpline number given on the reverse of the card and have it blocked. 
Since I know the police are useless would take no action, I did not go to the police station.
I however, called up the credit card helpline number and had my card blocked and also asked them to issue a new card.
Now, I am wondering how these people came to know that I had just received an SBI Credit Card.
It just means that someone from the SBI is involved in passing this information to these scamsters.
Further, I do not find any online contact details of police or any other investigating agencies to whom we could forward the contact details from where we receive these scam calls so that the people are caught.
If you try to call the above numbers now, they are either not reachable or switched off. It only means that the numbers are one way.They can be used to make call but cannot be called.
QED.