I put 2 of these portable immersion 2kw heaters in my 650 upright tank overnight, I put them on separate ext reels but still managed to melt a plug the other week, when I was replacing the plug I noticed there was no earth wire in the cable, could this be a problem?
No it wouldn't. Fully insulated electrical equipment doesn't need an earth. It it was an element fitted to a metal urn for example, then yes, it will need an earth.
It would have melted as there was a resistance at the plug point. That resistance would cause a hot spot. As the hot spot gets hotter, the resistance increases until something gives. It could have been a lose connection on the plug, on a poor connection on the extension cable's socket.
Using the correct size cable on the cable drum is important. Even more so is to always fully unwind the cable from the cable drum and lay it out as straight as possible. This will prevent the coiled cable generating a magnetic field when high current is used. The magnetic field will also cause heat, then resistance and could/will melt the whole cable. Seen it often on building sites overseas in the power tool industry.
Laying your cable out will also help to keep the cable cooler under load.