Ring the local authority/borough - they may accept your address for application now or may not until you are actually living there. Either way yours will be a late application as initial allocations for Reception entry in September are due to be published about now. There will be a space , just maybe not at a school you would have chosen or nearby.
What to do? Will there be place in the school and what can be done before I get to London. British so have an address already in North London ? Daughter will be just over 5 and first time in London for her.