There are important goods Chakrabarti cannot have for all kids while private schools are in place (such as a level playing field when it comes to careers in journalism, the civil service, etc.etc.). So Chakrabarti argues against private schools. However, for her not to buy private schooling for her own kids may, under the present system that does allow and encourage private schools, be to significantly disadvantage them. In which case it may be morally permissable for Chakrabarti to buy private schooling for her kids if she can afford it, notwithstanding her moral objection to private schooling.
Having said that, some very principled folk won't buy private schooling for their kids even if they do think that will likely disadvantage those children. That may or may not be beyond the call of duty. I am not going to condemn anyone either way.
Independent report here.