M.B.
J.,
We have flown to london with our daughter 2x. She is 17 months old. My first bit of advice - if you can afford it - get her a seat. Holding a baby for 9 hours....makes it feel like 18!
Flights to London are generally easier than the flights returning as you are flying overnight and you hopefully get the benefit of bedtime on the flight there.
Also, once the attendants are done serving, let your baby walk (or crawl) the aisles. Burn off energy. I guarantee people will most likely be receptive to your child, make conversation with the baby and you. And walking the aisle is better than kicking the seat in front and screaming because of frustration of being restrained.
People have also suggested taking some the baby's toys and putting them away until the trip - then they seem new on the day of the trip.
I will also warn you London does not have a stroller friendly public transport. Be prepared to carry the stroller down stairs and get over your apprehension of having the stroller on an escalator. Some tube lines have elevators, but more do not. Taking the bus is better. Check out tfl.gov.uk. That site can help you get from point A to point B and you can choose "bus only" as an option.