When DD first started school, getting her up was an hour before we needed to leave. Bags and lunches were prepped the night before, bags and shoes by front door, coats and keys in appropriate place, dining table set for breakfast, uniform including socks and pants hung on outside of wardrobe. I'd get up first and get myself ready, then wake DD and get her dressed (or just move clothes from wardrobe to bed and assist where necessary) and do her hair whilst OH got ready. All have breakfast together, I'd go off to work by 8:15. OH would then clear breakfast things, put lunch into school bag, make DD use the toilet, help her brush teeth and wash face, put shoes and coat on and leave the house by 8:40.
Once she got more independent, the routine would be the same but there'd be more shouting e.g. put your shoes on, they're by the door, the front door, this front door, HERE, put them on, other way round, no the other way round, OTHER WAY ROUND. You get the gist.
Given you don't have to be at work elsewhere, couldn't you load the washing machine the evening before, and just turn it on in the morning after breakfast? It'll be finished when you get back from the school run and you can hang it out then? I have a timer delay on mine, so load it the night before, and get up 15 minutes earlier to hang it out. I am not a morning person though so treasure every extra minute in bed.
Set timers if you need to. When DD got a bit older, we'd leave her to finish eating her breakfast, but given the chance, she'd take half an hour over it. So an egg timer for 5 minutes would let her know that once it went off, she had to come upstairs to brush teeth. Even though she could tell the time (certainly to the quarter past / half past) she'd end up in a little dreamworld, so this would pull her back.