Just fyi - the APD has been abolished for kids < 16 years old for flights departing the UK. Some airline websites will automatically remove that tax, but some (Lufthansa for example) tell you in small print to call their service center to claim a refund. So be aware that you might be due a refund.
It has taken a couple of weeks, phone calls, being passed around from department to department with Lufthansa until FINALLY...I spoke with a lady at Lufthansa who said "of course" she knew about the APD. Once I spoke with her, sent email to the correct Lufthansa department, touched base with Lufthansa Facebook page asking why no one had responded to my email. Then one day I get a reply asking me for documentation about the kids' ages. Gladly I sent all of that off to the person who requested it. Of course didn't hear anything after that until again when I sent another email asking for confirmation that they received the paperwork. THEN - Lufthansa finally acknowledged they received it and will be processing my refund in 14 days.
So 14 days from today "hopefully" I'll get my refund. Just be aware that it's not an easy path to navigate!