Flights from LCY (London City) are all with BA CityFlyer and uses Embraer aircraft which have 2+2 rather than 3+3 seating, so there is no middle seat. In Club Europe BA sells all the seats. In fact the differences in Club are minimal as there is also no lounge at City (they basically amount to a more substantial meal, a slightly wider bar selection, larger baggage allowance and additional Avios and tier points).

Even on BA mainline flights from Heathrow and Gatwick you are not guaranteed to be able to take a car seat on and use the middle seat. I had mine gate checked in April trying to do this (reason ‘there is a table in the way’, despite me pointing out that the tables fold away and it was a Neo aircraft without a table anyway). However I think the more junior staff member was more sympathetic, so I think it depends on the member of staff.

Incidentally I believe the car seat actually goes in the window seat with the adult then occupying the middle.

I am not sure on pricing, however I assume the pricing would be the same as an older child.