I am very disappointed with the Cheese Fondue recipe - we followed it to the letter and the cheese split and could not be saved whatever we tried. More detail and explaination might have helped. Shame as the taste was lovely!
Cheese fondue, such as Nigella's Cheese Fondue (from Nigella Express and on the Nigella website), is usually a fairly easy dish to make and if the cheese has separated it is usually because the heat used to melt the cheese was either too high or too low. A medium heat is usually about the correct level to melt the cheese without burning it, but if you have been heating the fondue for a while and it is still quite runny then try raising the heat a little. The cheese should be shredded, grated or cubed into fairly small even-sized pieces so that they melt evenly. The cheese and wine mixture should also be stirred slowly but constantly as it is heated.
A dry, slightly acidic wine is best for fondue as the acidity helps to denature and separate the protiens in the cheese, giving the fondue a stringy quality. If the fondue has been over-cooked and the cheese is turning into hard lumps then adding a teaspoon or two of lemon juice should help to restore the texture. If the cheese has split and looks greasy but not lumpy then adding extra cornflour (cornstarch) will help to re-emulsify the mixture. Mix a tablespoon of cornflour with a tablespoon of cold water and stir this into the fondue a little at a time, until the fondue comes together. You could also try tossing the grated cheese with the cornflour from the recipe before making the fondue as this can help to keep the mixture more stable.