Nanostructures of platinum-carbon nanocomposite material have been formed by electron-beam induced deposition. These consist of nanodots and nanowires with a minimum size ~20 nm, integrated within ~100 nm nanogap n-type silicon-on-insulator transistor structures. The nanodot transistors use ~20 nm Pt/C nanodots, tunnel-coupled to Pt/C nanowire electrodes, bridging the Si nanogaps. Room-temperature single-electron transistor operation has been measured, and single-electron current oscillations and 'Coulomb diamonds' observed. In nanowire transistors, the temperature dependence from 290 to 8 K suggests that the current is a combination of thermally activated and tunnelling transport of carriers across potential barriers along the current path, and that the Pt/C is p-type at low temperature.