desperate search for a secondary school

[NewLondoner1]

We're moving to London in June from another country due to my DH's job and we'll have our residential permit just in May.
Our DD has to attend a secondary school in Sep, 2018.
However, all the application and the admission period will be completed when we arrived.
In the first place we prefer state schools but when we understand that it's really impossible to be able to attend to an outstanding or good school,
we've just started to consider also the independent schools. However,
they also seem to have completed their registry procedures.
We think about another option: our DD was born on the 1st of Sep in 2006.
She's at the 6th year now. Is it possible for her to enroll to 6th year in the UK in Sep 2018
instead of the 7th year and then next year, we'll be able to apply for an outstanding secondary school in our catchment area.
We have to live near Heathrow Airport because of my DH's travel necessity.
What do you recommend us? We feel very much desperate. Thanks a lot.

New Londoner, please be wary of dome of these suggestions.one suggestion has been a junior school, rather than secondary. Other p suggestions would be a nightmare commute for a year 7 child. We live in Ha,Paton, and DD1 will start year 7 in September.

The suggestion that there are lots of Catholic schools in Hounslow/Sunbury/Eichmond area also smacks of a lack of local school knowledge. There is one Catholic secondary for the whole of London Borough of Richmond and it is oversubscribed (we were lucky enough to get a place, but DD got sibling preference as her brother is already there)

St Pauls in Sunbury has said they will take all practising Catholics and are not requiring a Certificate of Catholic Practice this year. But I don't recall you saying you are Catholic?

AuditAngel actually there are several Catholic schools in that area and the admissions areas are not based on local authority areas, but on other criteria eg parishes, deaneries, catholic practice.
And there are non catholics attending the schools.