Flake the tuna into a bowl. Put the sweetcorn in a small saucepan and pour boiling water over to just cover it. Cook for 3 minutes and drain through a sieve. Rinse the sweetcorn under cold water and add it to the tuna. Stir in the mayonnaise until well mixed.
Spread the tuna mixture over the two bread bases. Arrange the cheese on top of the tuna. Press the bread tops down firmly on the filling.
Heat a heavy-based frying pan or ridged grill pan for 2 minutes. Add the breads and cook on a gentle heat for 3–4 minutes on each side, turning them carefully with a fish slice or tongs. Wrap the tuna melts in nonstick baking paper and chill in the refridgerator until ready to serve.