We took a car seat on a TATL flight. No issues going to LHR. Upon return, the LHR-based FAs made a stink about our car seat not being certified by the European equivalent of the FAA. I showed them the DOT and FAA stickers, no dice. I told them I flew over with it and didn’t have an issue. They wanted me to hold my infant in my arms during taxi and takeoff. I told them that was less safe than the car seat.

I asked them to confirm that with the lead FA. By the time the lead FA showed up, we were pulling onto the active runway. She said “just buckle her in to her seat”. I got a nice apology and an extra round of drinks from the lead mid-flight.

Long story short, OP will be fine. Buy the lightest car seat you can find and a car seat bag. Carrying those things through an airport is a nightmare.