I see very different attitudes here between Brit and US.
Generally speaking, being left wing in Britain means not believing that money should buy advantage in education or health. These two should be available to all, at the best quality, when needed, is the creed. Abbott put herself up for election and asked for people's votes as a member of a party whose members would generally agree with the above premise.
She got the votes and represents a very poor area of London. By becoming an MP she qualified for a high salary that now enables her to pay school fees of £10,000, a figure far beyond the reach of her constituents.
By sending her child outside the State school system she is betraying her voters and their beliefs and hopes. She should resign her job as an MP and finance her betrayal some other way.
Otherwise she is a hypocrite.