I did this trip back and forth about six times when we lived in the US. I only had one child at the time, which made it easier. This is what I took:
1 large wheeled suitcase
Buggy - essential in airport in case you're delayed or there's a long distance to walk. Get an 'umbrella' style. Very compact, lightweight, but functional.
Baby Carrier
Shoulder bag with your stuff in it and all your travel docs, wallet, etc
Bag with all baby stuff in it. Spare clothes, bottles, snacks, toys, blankets. I had a canvas beach bag from Gap that was enormous (a nappy bag will not be big enough). No one ever said a word!
You can buy baby food and formula in Boots once you get through to departures. Take extra nappies - some babies get upset tummies on planes. Take plenty of muslins/wipes too and dummies if your DC like them. They soothe little ears on take off and landing (as does feeding).
How do you walk with all this sh*t? Child in buggy, baby in carrier, one carry on bag over each shoulder, wheelie suitcase dragged behind you. It's doable - just. I usually found someone to help me though. Good luck!