Hi. You may find that finding places for the older DC is not as much of a problem as you may fear. Families using the state sector tend to move from Central London as their kids move towards secondary age. (A combination of high house prices and concerns about secondary provision.) Others drift into the Private sector at 7+, 8+ and 10+.
You might contact school secretaries and ask about the liklihood of places in the years you need. Then pick a school and live as close to it as you can.
The same is true of private preps unless you are aiming for one with 7+ or 8+ entry points. Though there will be more interest from incoming ex-pats.
I have 3 kids, enrolled in a good NYC public school. I'm thinking of moving to London in the next 2 years - preferably Chelsea/South Ken/Notting Hill. I'm familiar with the issues such as shrinking catchments for popular state schools, faith schools, private v. public. In 2 years, dc #1 will be 10 (Y6), #2 8 (Y4) and #3 5 (Y1). Very interested in Fox Primary or the clutch of top C of E Chelsea schools. Has anyone been able to get their kids in at those stages? If not, what private school would you recommend - would prefer to save $ for boarding or Y7+. And what privates would be a good commuting distance from that area?