Heat the oil in a large heavy pan. Add the garlic, onion, celery, carrots and lemon zest, and cook for about 5 minutes, stirring all the time.
Add the lemon juice and the tomatoes with their juice, cover and cook over a low heat for about 25 minutes until the vegetables are very tender, stirring occasionally.
Meanwhile, scrub the mussels with a stiff brush and pull out all the hairy beards. Discard any damaged mussels or open ones that do not close when tapped on the work surface. Rinse well.
Add the fish and squid and a little water to the pan with the vegetables. Cover and cook for 3–5 minutes until the fish is just tender. Arrange the mussels on the top, cover the pan tightly and cook for about 5 minutes, stirring occasionally. The mussels should have opened; discard any that remain shut. Stir in the parsley and season with salt and pepper. Serve hot or cold.