Possibly only a minor effect.
CEA ceilings are revalorised annually anyhow, so even with the short notice introduction, they'll catch up.
And parents get 90% of permitted costs (can include some "extras", and its 92% if state boarding) up to the ceiling, meaning that if the school is more expensive than that the parents have to pay everything above. So yes, it might be difficult for those who have opted for more expensive schools.
And in percentage terms, the rise can be swingeing - the greatest being if your school costs £10k a term, and CEA covers 90% (just inside ceiling which is £9,080) then parents pay now £1k a term. But with a £2k a term rise (if passed on in full) and only £80 remaining within ceiling, then the new parental payment is £2,920 - which is still significantly less than what full fee-paying families have to find, but represents a nearly 200% rise.
But I hope they will revalorise in time, lifting the ceiling to around £10,800 ie 90% of a £12k fee (rather than roughly 90% of £10k where it is now)