Cache circuitry, a data processing apparatus including such cache circuitry, and a method for prefetching data into such cache circuitry, are provided. The cache circuitry has a cache storage comprising a plurality of cache lines for storing data values, and control circuitry which is responsive to an access racquet issued by a device of the data processing apparatus identifying a memory address of a data value to be accessed, to cause a lookup operation to be performed to determine whether the data value for that memory address is stored within the cache storage. If not, a linefill operation is initiated to retrieve the data value from memory. Further, prefetch circuitry is provided which is responsive to a determination that the memory address specified by a current access request is the same as a predicted memory address, to perform either a first prefetch linefill operation or a second prefetch linefill operation to retrieve from memory at least one further data value in anticipation of that data value being the subject of a subsequent access request. The selection of either the first prefetch linefill operation or the second prefetch linefill operation is performed in dependence on an attribute of the current access request. The first prefetch linefill operation involves issuing a sequence of memory addresses to memory, and allocating into a corresponding sequence of cache lines the data values returned from the memory in response to that sequence of addresses. The second prefetch linefill operation comprises issuing a selected memory address to memory, and storing in a linefill buffer the at least one data value returned from the memory in response to that memory address, with that at least one data value only being allocated into the cache when a subsequent access request specifies the selected memory address. By such an approach, the operation of the prefetch circuitry can be altered to take into account the type of access request being issued.