In the Autumn Statement, the Chancellor made the surprise announcement that Air Passenger Duty would be scrapped for children aged 2-12 years old from 1 May 2015. This only applies to economy tickets.
Since British Airways sells tickets a year ahead, there are plenty of people who booked flights between May and December 2014 for travel after 1 May 2015. BA has now released guidance for how these people can receive a refund on any APD paid for a child:
If you booked directly with British Airways the APD charge will be refunded back to your original payment card as soon as you have flown the outbound sector from the UK.
If you booked with a travel agent and British Airways processed the payment (ie BA appeared on your card statement and not Expedia etc) then the APD charge will be refunded back to your original payment card as soon as you have flown the outbound sector from the UK.
If you booked with a travel agent and the travel agent processed your payment (ie their name appeared on your card statement) then you must contact your travel agent once you return to the UK. British Airways is not automatically refunding travel agents so the agent must make a formal refund request on your behalf and then transfer the funds to you.
I feel this last one could be a slow process ….