Children Traveling from US to UK alone

What airport they're flying into.
What airline they're flying on.
What time they arrive.

What's their nationality?
Do they have valid passports?
How/where/when will you meet up with them upon arrival?
How will you contact them if something goes sideways with their travel?

First, contact whichever airline you will use and ask about their regulations for unaccompanied minors.

all of the above

These are the UK requirements for a Child visitor. (Not clear from your question though whether you are visitors or residents)

V 4.11 Adequate arrangements must have been made for their travel to, reception and care in the UK.
V 4.12 If the applicant is not applying or travelling with a parent or guardian based in their home country or country of ordinary residence who is responsible for their care; that parent or guardian must confirm that they consent to the arrangements for the child’s travel to, and reception and care in the UK. Where requested, this consent must be given in writing.

The check-in at the US airline's counter will determine if they can fly to London. SO -- check very carefully with the air carrier and understand their requirements for unaccompanied minors. If they are refused boarding then nothing else matters. Second, contact a British consulate or the embassy to determine what a minor needs to enter Britain. Good luck.

Have they flown without parents before ? Have they gone through Immigration (accompanied or not) ? Will one or both of you be at the airport in London if there are questions ? This part is more for your and their levels of apprehension.
As stated above, the big question is what does the airline require for unaccompanied minors flying to the UK ? You really don't want surprises when someone takes them to the departure airport and both parents are in London!

You need to roleplay situations like cancelled flights, security, immigration and make sure they have a working phone on arrival with which to contact you.