Thanks everyone for your advice! surprised to have so many replies!! I guess it's a popular topic... :-)
I just wanted to clarify: when I say I give her pizza I mean some passata on a sandwich pocket, topped with sweetcorn, peppers and mushroom so she is getting plenty vegetables. Also, when I do pasta with sauce, I make the sauce with tomatoes, peppers and onion and she has tuna or salmon with it. Tonight she polished off some homemade mince with veg through it along with carrot and parsnip mash, and had beans on toast for lunch. She also likes homemade quiche with cherry tomatoes and broccoli through it, and a family favourite is baked sweet potatoes with spring onion and tuna on top.
I do often give babybels for a snack, and have tried lots of other healthy options such as carrot/cucumber sticks and dip. The trouble is she knows what she wants, so will just howl and cry for cake (a bit of Soreen or a Goodies Carrot Cake Bar) until I usually relent. No amount of distraction will work!
I will certainly continue to try to introduce more protein, though she's never been hugely keen on chicken or other meat. Anyone suggest any nice recipes that their toddlers have enjoyed? I know it's no excuse but I find it very hard to find time to prepare food for her. We are at a stage when she spends most of the time clinging to my legs like a monkey when I am in the kitchen, shouting for food and pulling open cupboards to see what she can raid!
Very comforting to hear I'm not alone....it's very embarrassing going out in public when it's your child raiding the bins, then shoveling food in her mouth haha! I frequently hear the refrain "Do you not feed that child or something?!?" Even when I avoid the sweet treats at playgroups, she will hunt them out! There's no flies on her, as they say!
Also, are others with kids of the same age still giving them milk at bedtime?