In England the entry year of school is Reception. Children start in Reception the year they turn 5. That is, your child will start Reception the September after they turn 4. You need to apply before that and in London the deadline is usually in the previous January.
So in the September after her 3rd birthday make sure you are signed up for all your local state school open days/parents visits. Some have only one. Others run them weekly.
Each of your local schools will have admission criteria on their website. Typically first priority goes to children in care and armed forces. Second priority goes to siblings. Third category is distance with those closest to the school allocated first.
You need to find out where all your nearest primary schools are. Then do take a look at Ofsted reports but don't rely on those. You need to also visit schools. Ofsted is not the best basis for judging a school on its own. You need to get an idea of whether the school is right for your child.
Try this www.gov.uk/find-school-in-england
You can also find out from your local authority what the last distance admitted for each child was for that school in the last few years.
In London you apply through your local authority BUT all admissions are pan London so it doesn't matter what borough the school is in. They all go into one pot. I live on the edge of three boroughs in London but only need to put in one application.
Make sure you fill up all your preferences even if some are schools you don't really want. Even if you are confident you will get into your desired school. Freak admission years do happen - it is unusual but the class could fill up with all siblings one year and have no siblings another year! So put down a school that you may not want bit works for you eg on route to work, close by home etc that you know you'll get for sure as your backup.
Finally your child doesn't have to start straight away. In your case you can actually defer all the way to the summer term without losing your place. Handy if you get an undesirable school so you can keep your place and home school or keep at nursery while you are on the waiting lists.