Bring a large saucepan of water to the boil. Add the runner and French beans and cook for 5 minutes. Add the broad beans and cook for a further 1 minute. Drain and set aside. Wipe out the pan.
Heat the oil in the pan and gently fry the onion and potatoes, turning frequently, for 5 minutes. Cover and cook very gently for a further 10 minutes or until the potatoes are softened and beginning to colour.
Stir in the garlic, vinegar, mustard, sugar, bay leaves, tomatoes and tomato paste. Bring to the boil, then reduce and gently simmer, uncovered and stirring frequently, for 15 minutes until the sauce is very thick.
Add all the beans to the pan and stir well. Heat through gently for 10 minutes, adding a dash of water to the pan if the mixture runs dry. Season to taste with salt and pepper before serving.