Privacy is a major concern in designing any cryptographic primitive when frequent transactions are done electronically. During electronic transactions, people reveal their personal data into several servers and believe that this information does not leak too much about them. The adaptive oblivious transfer with hidden access policy (AOT-HAP) takes measure against such privacy issues. The existing AOT-HAP involves a sender and multiple receivers apart from a designated issuer. Security of these schemes rely on the fact that the issuer cannot collude with a set of receivers. Moreover, they loose security when run with multiple protocol instances during concurrent execution. We present the first issuer-free AOT-HAP in universal composable (UC) framework in which the protocol is secure even when composed with each other or with other protocols. A concrete security analysis is given assuming the hardness of q-strong Diffie-Hellman (SDH), decision Linear (DLIN) and decision bilinear Diffie-Hellman (DBDH) problems against malicious adversary in UC model. Moreover, the protocol outperforms the existing similar schemes.