Not invited to interview 13+

[pasok1000]

If we get a letter from London school not invited to the interview, are there sometimes cases when list moves within year 6 and u get invited?

Which London school? A selective independent? I don't believe so as I think any movement comes from the waiting list of children interviewed. You can ask the school and also could ask for feedback/how close/is it a definite no etc.

I would say that if your child hasn't been invited to the interview, then the process is closed. The London schools in particular are highly competitive with hundreds of applicants for very few places.
Do you have other schools on your exam list?

They will already have more invited to interview than they plan to offer a place to, and offer more places than are available on the assumption many apply for more than one school. Sorry but very unlikely your dc would be considered for a place later on.