They didn't underestimate...

They always knew it'd cost £10bn. It's just that if they said it'd cost £10bn from the start, it would never have got any support.

So, they said it would cost £2bn, with lots of private funding contributing much of the cost, so everyone says "Oh, that's not too bad."

Then, when it's too late to back out they tell us the real cost, that they knew all along.