Spread 1 side of each bread slice with butter. Turn over 4 slices and spread with chutney, then divide cheese and bacon among them. Top with remaining bread slices, buttered sides up.
Heat a dry 12-inch skillet over moderate heat until hot, then cook sandwiches, 2 at a time pressing occasionally and turning over once, until bread is golden brown and cheese is melted, about 5 minutes per batch.