Another way to do salmon on a barbie is to hot smoke it. It’s a bit of a faff, but worth it - but too much hassle if you’re taking it to someone else’s barbie!
The recipe I use:
Start with a whole side of salmon, skin on. Mix 1 large cup of salt and one of sugar. Cover the salmon with the salt/sugar mix, put in a bag, leave in fridge overnight. The salt/sugar mix will cure the salmon and draw the liquid out
Next day, the salmon will be covered in a slimy salt/sugar gunge. Quickly rinse it off and pat the salmon dry. It’ll be quite firm and red.
Now the fun bit.
Old baking tray, with a layer of foil on top.
Put a couple of spoonfuls of Lapsang Souchong tea leaves on the foil (I use about a dozen tea bag worth).
Wire rack above that, then salmon, skin-side down.
Fold the foil up to make a sealed tent over the salmon. Make sure it’s sealed all round.
Put it on the barbecue for about 20 mins, to smoke it in the tea smoke.
Serve hot or cold with crusty bread and ginger butter.
While you could conceivably cook this on a hob, you house would stink for weeks.