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New Labour was a departure from Old Labour, a move towards the centre, even past it but it wasn't Thatcherism. It didn't believe in the continued shrinking of the state and the absolute efficiencies of the free market.
It was a pragmatic, centralist party. The logical conclusion to the beliefs of Thatcherism is the abolition of as much government supported services as possible. That's the NHS and education. I seem to remember New Labour ploughing money in to these things. Even improving them in its own ham fisted, target setting ways.
Is this so bad when the only real alternative is the Tories?
Yes, but if you want to have any influence to change things for the better you will need to be in power. In a 2 party, first past the post system then you will need to reflect and support a large segment of society's wants and needs. This means compromise. This is what New Labour did. The alternative to New Labour was continued Thatcherism. If you thought that this shrinking of the state is painful, imagine if continuation of the politics of 80's was allowed. The county would be far further gone than now.
If you want to be in the frame to improve things then you have to be pragmatic.