We present 30-GHz Sunyaev-Zel'dovich (SZ) observations of a sample of four galaxy clusters with a prototype of the One Centimetre Receiver Array (OCRA-p) which is mounted on the Torun 32-m telescope. The clusters (Cl 0016+16, MS 0451.6-0305, MS 1054.4-0321 and Abell 2218) are popular SZ targets and serve as commissioning observations. All four are detected with clear significance (4 -6σ) and values for the central temperature decrement are in good agreement with measurements reported in the literature. We believe that systematic effects are successfully suppressed by our observing strategy. The relatively short integration times required to obtain these results demonstrate the power of OCRA-p and its successors for future SZ studies.