Mix all the dressing ingredients with a little salt and pepper and 2 tbsp water until well blended. Halve or thickly slice the potatoes if large and boil for 7-8 minutes in a pan of salted water with a steamer full of beans over the top until they are both tender. Cool them separately under the cold tap.
Pile the potatoes into a bowl followed by the beans and peas. Just before serving, peel, stone and chop the avocados and toss with lemon juice to stop them discolouring. Pile on top of the salad and drizzle over the dressing.
Cover the bowl with cling film to transport. Toss just before bringing to the table to mix and coat everything in the mayo dressing. If you have a long journey or want to make this a day ahead, prepare and add the avocados and lemon juice.