Clean the squid and pat it dry. Cut the tentacle part in half or quarters lengthwise (and any longer pieces cut into shorter lengths) and slice the main body, including any flaps, into rings around ⅓in/1cm thick.
Prepare a bowl with iced water then add the squid to a pan of boiling salted water (a 4-5 quart pan, around half full with water and about ½-1tsp salt should be good) and cook for around 40-60 seconds until it goes opaque. Remove from the pan with a slotted spoon or strain into a colander then immediate place in the iced water to stop it cooking any more.
Meanwhile cut the fennel in half then into thin slices, including a little of the green fronds if you like. Slice the red pepper, cutting any larger slices in half, halve the tomatoes and roughly chop the leaves from the parsley. Peel and dice the avocado.
Place all of the chopped vegetables and squid in a bowl. Whisk together the lemon juice, vinegar, oil, mustard and a few grinds of salt and pepper and pour the dressing over the salad. Carefully toss everything together and leave for a good 15min or so to take on the flavors a little before serving. You can also chill it a good few hours until you are ready to use it.