When to start 7yo – end of year 2 or start of year 3?

[newschoolneeded]

I’m a returning ex-pat and DD hasn’t ever been in school in the UK. She finished year 1 at her school abroad and we’ve had to travel for work and been home-schooling since last summer – so most of what should have been her year 2. We will be coming to London but the date and location is flexible and what’s best for her enrolment might become a factor.
I’ll need to put in an “in-year” enrolment for her, and the borough placement teams don’t want to hear from me until we actually arrive. We’ll be renting, or in an airBNB until we can find a suitable longer-term option. It seems like we will just have to put up with what-ever school in the area has a vacancy. I’m not sure of the most efficient way of tackling this. I don’t have any strong feelings about where to live.
Our original plan was to move back to her old school abroad for the last term of year 2 where she is still enrolled but will have missed most of the academic year. Then we’d use the summer holidays to relocate to London and find her a new school.
Now I wonder if we should just get to London asap and try and get her into a school for summer term there. Does anyone know if we are more likely to find a good in-year placement for year 2? Do any kids transfer out of primaries into juniors, leaving vacancies in primary year 3? Will all the placement teams be on holidays over the summer anyway?

Yr3 has the advantage of no class size limit.
Depending on area, there may be places come available as some move into Prep schools or out to the suburbs/surrounding counties.
But... there is also the issue of admissions not working over the summer.

If you can arrive around late May, they could offer you places for September (some areas do this not all). Gives you time to be on Waiting Lists and find a permanent address while continuing home education

Good luck... In Year admissions rely a lot on luck!

Thanks @PuttingDownRoots that's helpful - I thought it might be down to luck! At least that's a bit reassuring that I shouldn't put too much energy into solving a problem that's probably mainly out of my control.