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Cut the tentacles off the squid and put in a bowl. Slice the squid tubes into roughly 1cm thick rings and add to the bowl. Heat the oil in a large heavy-based pan over a low heat, ensuring it is no more than two-thirds full.
For the aïoli, mix the mayonnaise, garlic, saffron and lemon juice in a small bowl. Set aside.
Toss the squid with the flour, cornflour, baking powder, cayenne and ½ tsp salt. When the oil has reached 170C on a thermometer, or when a cube of bread is dropped in and turns golden brown in 30 seconds, deep-fry the squid in batches for 2 mins, or until lightly golden and crisp. Set aside on a tray lined with kitchen paper. Serve the fried squid with the aïoli on the side for dipping.