Calling their bluff was an option, I doubt the 456 would have wiped out the planet as they threatened. Not that I doubt they could have. They have intersteller travel, the ability to control (in a limited way) the children of an entire planet from distance, and they had the ability to release a lethal toxin at will...of course we have no way of knowing how lethal it would be outside of an enclosed space like Thames House but would you want to bet against it? I suspect the 456 response would have been to slowly up the ante. Much as the junkie mugger maybe doesn't shoot you right away if you refuse to give him your wallet, perhaps he pistol whips you first. So perhaps they wipe out a city, then another. Eventually one of three outcomes occurs.
1. The 456 say "sod this for a game of soldiers" and bugger off leaving the earth intact. (The junkie mugger runs away)
2. The 456 say "sod this for a game of soldiers" and bugger off blowing the Earth apart first. (The junkie mugger shoots you then runs away)
3. The people of earth make a colective decision to salvage humanity at the cost of 10% of their children. (You wife shouts "Oh for god's sake give him your wallet, Charles." The mugger takes your wallet and runs.)
At the end of the day all the talk of fighting them and retaining moral integrity is rubbish. Some people would, yes, but the majority would cave in. Throughout history small weak nations/ towns/villages have been pillaged by those stronger and more vicious. Some fought, but I suspect most gave the brigands what they wanted. The village elder sacrificing his comliest daughter to save his other three children. Is it self perpetuating, yes, the brigands will always come back until you are able to fight back, you die, or they find richer pickings elsewhere.
It isn't nice, it isn't fair, and maybe Jean Luc Picard wouldn't approve, but that's the reality of the situation. And its not even like we had anyone to fight. Unless the 456 in thames House was the only one, then you have to assume there are plenty more. They might have a whole battle fleet, or they might have one scout ship, but if you can't see it you can't hit it.
Is it right to comdemn 90% of the world's children to death for moral integrity? That's what I adore about Children of Eearth. RTD and co created a scenario for which there was no real solution.
Fight back and maybe you all die, or maybe the 456 run away.
Give them the children and they will return, but maybe you're ready for them next time, assuming civillisation doesn't collapse into anarchy in the meantime.
Of course I'm looking at this at the big picture level, ignoring the fact that these are children being sent to a hellish fate, but I guess thats what the world leaders had to do, look at the bigger picture. They way the British (and probaly most other) governments went about it was shitty and they should be punished for the decisions they made about how to fill the 456's order, but I don't think they can be castigated for choosing the lesser of two evils when it came to giving in.
Perhaps I'm too optimistic about humanity as well, because I don't think the loss of 10% of our children would have destroyed humanity. Altered it, yes, quite radically, and probably not in a good way but destroyed it, no. Millions died in WW1, WW2, 50 million in 1918 from Spanish flu, but we're still here.
And the 456 was right, we let kids die everyday, because we don't care, because we want cheap clothes and cheap food, because we don't want to give up our wealth, becacasue we're too busy arguing about things on the internet

, all the 456 were doing was making us make the decision to kill them conciously, and making us make the decision about our kids, not the ones in poor countries. (I still think RTD missed a trick. Nick Brigg's character should have said something like..."you know there are X number of children in Africa...")