Dd was exactly the same as yours, and we are still late on occasion now, but only two or three minutes, so everyone is still sauntering into the building.
Firstly, tell the teacher and the TA, it will help enormously to not have them tutting at you too often.
Secondly, don't get her up too early. There needs to be no time for tv/playing, as that will go totally downhill. Tiredness excentuates (sp?) the situation, so early bedtimes too.
Thirdly, bring everything into the room she has breakfast in. Dd can't get dressed before breakfast, as she misses her mouth too often. Set a timer for ten mins, and as soon as the timer goes off the breakfast bowl gets taken away. She will soon learn that she will be hungry by 9.30 unless she speeds up. I hated this bit as I am a huge believer in getting a good breakfast, but it was necessary and worked very quickly. Once she has eaten, do teeth over the sink so no toothpaste goes down the uniform, and then uniform on. If she is confined to the breakfast room then she will not be able to get distracted with toys and pens etc.
You need to be fully ready before you get dd up. You need to be next to her the whole time, constantly cajoling her and egging her on. Heap on the praise - "you are such a clever girl, I am so proud that you are my daughter, if other parents could see how well you do in the mornings they would be so jealous!", and if she kicks off then "I bet xxxx would never behave like this. S/he is always in school on time, what would s/he think if s/he saw you behaving like this?" Or "Mrs XX would be so sad if she thought that you hated school so much that you didn't want to get there on time. She tries very hard to make sure that you are having fun. If we are late she will want to know why, and I will have to tell her that you didn't want to get dressed". Then if there are reasons for hating school they come out at that point, you come up with a way to solve them, and dd is feeling much brighter and more willing to comply.
If she won't get dressed, she goes to school in pj's. Dd's teacher and TA were so horrified that she turned up in her pj'sthat she turned up in her pj's (they were acting as they knew that situation, but made a huge fuss re. how they thought she was more grown up than that!) that she would let me dress her for a few months. Then it would slip, she would go in in pj's and it would start again. Now we have no probs.
A routine helps massively, and it does get slowly easier. I always worry at the end of holidays that this time her will will be too strong, but now I need to be on a train as soon as I have dropped her off she knows that there is no messing around!