A data processing apparatus and method are provided for controlling access to secure memory by virtual machines executing on processing circuitry. The processing circuitry executes hypervisor software to support the execution of multiple virtual machines on the processing circuitry. A memory system is provided for storing data for access by the processing circuitry, the memory system comprising secure memory for storing secure data and non-secure memory for storing non-secure data, the secure memory only being accessible via a secure access request. Address translation circuitry is responsive to an access request issued by a current virtual machine specifying a virtual address, to perform an address translation process to identify a physical address in the memory, and to cause a modified access request to be issued to the memory system specifying the physical address. A trusted virtual machine identifier is maintained and managed by the hypervisor software, with the hypervisor software setting the trusted virtual machine identifier if the current virtual machine is to be trusted to access the secure memory. Accordingly, in response to the access request issued by the current virtual machine, the address translation circuitry is only able to cause the modified access request to be issued as a secure access request specifying a physical address within the secure memory if the trusted virtual machine identifier is set. By such an approach, the hypervisor software is able to support multiple virtual machines at least some of which have access to secure memory under conditions controlled by the hypervisor software.