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Put the potatoes in a pan of boiling water, bring back to the boil and simmer for 8-10 minutes until tender.
Meanwhile, mix the pesto and oil to make a dressing. Halve the tomatoes, drain and flake the tuna. Add the beans to the potatoes for the last 3 minutes of cooking time.
Drain the potatoes and beans and tip into a salad bowl. Stir in the spinach so that it wilts a little in the warmth from the vegetables. Season with salt and pepper. Scatter the tomatoes and tuna on top, drizzle with the pesto and gently toss everything together.