Banks are having the last laugh even as they reduce base rates, because they won't lose money from customers who should, but won't see a rate cut. For some of the banks the rate that should "float" - that is, have borrowers pay less interest when the base rates fall - are not going to. For you as a home loan borrower, you should think twice before rejoicing that after SBI, even Axis Bank, ICICI Bank and HDFC Bank have cut base rates; the cut could probably not apply to you.
In particular, Home loans that you "thought" you got from HDFC Bank may not at all change rates. You see, you go to the bank, the banker sells you the loan, you sign the documents and give your money. But you don't get a loan from HDFC Bank - you get a loan from it's group company, the big daddy Non-Banking Finance Company called HDFC. This is a different company altogether, and as an NBFC does not even need to have a "base rate".
To understand this better, let's change the name of HDFC (the non banking entity) to "XXXX".