DD does. She's in reception and has largely rejected school food so takes pack ups most days. Nursery conditioned her to expect pudding after most meals and the rest of her class on school dinners get one too so I'm happy for her to. I get the point about school/nursery desserts being lower sugar but 2/3/4/5 yr olds don't care. Besides, if she's going to have sugar then a small amount after a meal is far better for her than a chunk mid-afternoon with nothing else to balance it out!
She tends to get a small cookie, custard cream, homemade oaty biscuit or homemade banana and apple mini bun cake type thing each day.
Otherwise she either takes either a sandwich (on a wholemeal roll), cheese cubes or chopped up sausage, fruit/veg pot and yogurt or pasta with homemade veggie sauce, chopped up sausage/grated cheese with a fruit/veg pot on the side. I would like to be able to do chicken or tuna or something instead of the sausage but she doesn't like much meat so it's cheese, sausages or beans for protein at lunchtime as I can't put nuts in so it will have to do.
She also takes a pot of fruit/veg for break time snack, and another one for after school club - mix of carrots, pepper, cucumber, peas, sweetcorn, grapes, apple, pineapple, strawberries etc. depending what's in season etc. She'll also have a rice cake, oat cake, cracker or something for after school too to go with the fruit/veg.
Overall her meals are balanced so a small piece of something sweet is hardly going to hurt.
We're lucky her school have a very pragmatic approach to lunches and don't have an official policy other than to promote healthy eating. They periodically remind people what a health lunch box might look like. The only rules are no nuts as the school is nut free and no fizzy drinks. Apart from that they say recommend no chocolate or sweets, not chocolate spread or jam on sandwiches, ideally no crisps and only include sausage rolls etc occasionally at most.
For the poster who said about apple going brown - we just toss it in a splash of fruit juice, then dry it off before it goes in the pots and it's still good til break or lunch. We learnt that trick when a wobbly tooth made whole apples tricky!