The difficulty our country/politicians face is that whatever we do will then be publicised and instantly accessible in these countries that have turmoil.
Reason why this is an issue?
If you had kids and find out that if you were to travel to the UK with your kids the UK would accept your child and send you back. Your child would then be relatively safe and have a thousand more opportunities in life. This journey would be attempted En masses. Particularly in war torn countries.
I still believe that the kids should be allowed in however if I was a politician the logistics of child care is a major factor alongside the then oncoming wave of children we would then have to accept and for the sake of the country unless told otherwise I'd likely decline.

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Oh and that type of policy would lead to other European countries pushing child refugees to the UK as well, it's morally easier and cheaper than sending them home