Handling school after a move?

So we recently moved last minute, and are now wondering what's the best route to take regarding school.

My child is starting reception this year. We filled in the application from the last address. From what I've seen, if we now apply in the new borough, they could be given any school. The two schools nearest to us look fantastic but are oversubscribed.

The schools in our previous borough were all fantastic too, and it's likely they'd get a space in one of them. They are only a 15 minute drive away, but ideally I would have preferred to walk to school everyday. Plus I'm due baby 2 in July, making a car journey even more undesirable.

My main worry is that they get given a school that isn't as great and ends up being a drive away anyway.

What do you think you'd do?