London City Airport is probably my favourite London airport. It has a small play area near gate 5 and baby-changing and breastfeeding rooms with a changing table, sink and armchair. What makes it especially child friendly, though, is its size. Queues are rarely long and it is very easy to navigate.
The oversized-baggage desk is beside check-in. At the right-hand security station we did not need to remove liquids or even take the baby from the pushchair. There is also a small pharmacy with baby essentials after security.
Although an accessible route exists, pushchairs often have to descend about fifteen steps from the waiting area to the tarmac. They are folded before going downstairs and handed to the crew; on arrival they are usually collected from a baggage belt.
Not every destination is served, but given the choice I would always use London City, particularly when travelling alone. The smaller aircraft have two seats per side—so a couple with a baby, or one parent with a toddler, has no stranger sharing the row.