Preheat a sandwich press or large skillet over medium heat.
Stir the chutney, mustard, and Worcestershire in a small bowl.
Butter one side of each piece of bread.
Spread the chutney mixture on the unbuttered sides. Layer cheese, ham, and tomato. Season with pepper and a pinch of salt.
Close each sandwich with bread, buttered sides facing out.
Toast in the press until deep golden and melty, 3–4 minutes. For a skillet, cook 3–4 minutes per side, pressing lightly.
Rest 1 minute on a board, then slice and serve hot.