Neha,
In London if you are planning on hiring a private taxi you will need to use a car seat as it is illegal for a child to be in a car without car or booster seat.
If, however you are just planning on getting a black cab from the street and you have a child who fits in a stroller it will not be necessary as the stroller fits in the back if the car with child still in it as they are all wheelchair friendly so there will be no need for a car seat at all. The stroller will fit on most forms of public transport like the underground and buses also.
If you have any more questions please feel free to ask.
Hope this helps,
Amy