Right here goes
Asparagus - basil, Parsley, tomatoes
Aubergine - beans, Maragold
Basil - Pepper, tomatoes, marigold
Broad Beans - brassicas, carrots, cucumbers, herbs
French Beans - Cucumbers, potatoes, pumpkins, sweetcorn
Runner Beans - Pumpkins, sweetcorn,
Cabbage - celery, onions, garlic, peas, spinach
Carrots - Chives, leeks, lettuce, onions, peas, sage, tomatoes
Celery - Beans, onions, cabbage
Melons - Beans, nasturtium, peas, sweetcorn, sunflowers
Leeks - Carrots and onion
Lettuce - Carrot, radish, strawberry, cucumber
Onions/garlic - Beets, carrots, lettuce, cabbage
Parsley - Asparagus and tomatoe
Pea - Beans, carrots, cucumber, radish, sweetcorn, turnips
Peppers - Basil
Potato - Beans, cabbage, marigolds, cucmbers, sweetcorn
Pumpkin - sweetcorn, marigolds, nasturtium,
Tomatoes - Asparagus, basil, cabbage, carrots, onions/garlic marigolds, parsley
Turnips/swede - Peas
Hope this helps - it worked for me last year, especially the carrots and leeks but whether that was the companion planting or just basic good luck, who knows. Am doing it again this year on a larger scale, so will keep you posted.