Put the potatoes and turnips in a colander and rinse under cold water. Set aside to drain, then transfer to a clean tea towel and squeeze out any excess moisture.
Heat the oil in a deep-sided, heavy-based saucepan until a breadcrumb sizzles and turns golden-brown when dropped into it. (Caution: Hot oil can be dangerous. Do not leave unattended.)
Carefully lower the potato and turnip slices, in batches if necessary, into the hot oil and fry for 2-3 minutes, or until crisp and golden-brown. Remove from the pan and set aside to drain on kitchen paper. Sprinkle with onion salt. Serve immediately.