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First, a fact that has escaped many people. LBB cannot open a new school. New schools have to be Free Schools or Academies, and their buildings are funded by Central Government agencies. New classes at existing schools are funded by Barnet.
Schools that have accepted additional classes can do so again, but probably only after their 'bulge' class has left (which for a primary school is 7 years later) or they have expanded to take an extra class in each year-group - as happened in St Catherine's. None of the three schools at the top of the hill (Monken Hadley, Christ Church and Foulds) can expand unless they move, as the sites are too small, and/or roads are too congested for safety.
Thirdly, some of your correspondents may be interested to know that Christ Church school is oversubscribed partly because people from outside the CofE would prefer a faith-based education even if it is not their own faith, and Jews, Muslims, Hindus and Buddhists learn alongside Christians of all denominations, and those whose parents are atheist or agnostic.