I collected some cockles from the beach today and would like to try cooking them tomorrow. In the meantime I have soaked the cockles in tap water and I have added some salt into it. I have not put them in the fridge. Is this the correct procedure?
A general advice upfront: make sure that cockles in your region at this season are safe to eat as shellfish tend to accumulate potential harmful substances in their tissue.
Cleaning with seawater
I (or already the fishermen that collected the cockles) usually put them in a container with seawater which was changed every five or six hours. The more often you repeat this procedure the less sand you'll have in your meal (however, even in restaurants it is not uncommon to find a bit of sand). You don't want to keep them in there longer than a day though. Keep them out of direct sunlight. Refrigeration generally is not necessary for half a day to a day. Afterwards discard all individuals that are open (= dead) and use the remaining cockles to prepare your meal.
Cleaning with freshwater
I have never put them into freshwater, therefore here only a guess: theoretically you can simulate seawater by adding the right amount of salt. You'll miss all other elements though, including nutrition, and therefore will generate stress for the cockles which will likely impede their ability to filter water (= clean) and survive. I advice you to use seawater if you have access.
A Portuguese recipe includes white wine, a fair amount of garlic, parsley and olive oil. Heat the olive oil in a pot, cut the garlic in half or quarters (not too small) and add them to the pot. Once they are precooked add the cockles and the white wine. Put a lid. Once the cockles are open they are ready to eat (some will not open - Discard closed cockles). Add the parsley when nearly all the cockles are open and cook for a minute more. Eat them straight out of the shell, maybe with a bit of lemon juice. Use bread to enjoy the cooked white wine mixture. Eat the garlic, it should taste delicious.
Used to collect these all the time as a kid in the summer holidays with my Grandparents. The method they always used was to to give them a good rinse in tap water, then leave them in a bucket full of tap water overnight and add some flour to it for them to feed on to help get rid of the grittiness.
As always, discard any open ones prior to cooking, along with any that don't open during cooking.
They'll die quickly in fresh water with or without "salt" added. Seawater with a cup of cornmeal added and mixed around (irritates them and they spit it out along with all the sand in a nice goopy mess), and change the water a couple of times a day. Not the best eating clam as they're mostly foot and pretty chewy but works great for chowder.
Cockles love oxygen, not floured water, they purge sand and grit in sea water (water with sea salt, NOT table salt.) Change of water during purging from a cold fast running from a tap for maximum oxygen. Our local clams hardly need any purging.
The cockles I have just purged (South Devon UK) were all but one totally purged. However grit was still in the shell and cooking juice. Muslim Sieve would have cured this problem. I did three purges, some time in-between without water. Best results yet! Cockles are temperamental, size of purging bowl, water temperature may make a difference.