In a private car, the rule is straightforward: children must use a child car seat until they are 12 years old or 135cm tall, whichever comes first. Licensed taxis and private hire vehicles are the exception to that rule, and it catches a lot of parents by surprise.
The exemption works like this. If a child car seat is not available in a licensed taxi or minicab, a child aged 3 or over may travel in the rear seat wearing the adult seat belt. A child under 3 may travel in the rear without a car seat and without a seat belt. Children should not travel in the front passenger seat without appropriate restraint.
It is worth being clear about why that exemption exists. It is there so families are never stranded — not because travelling without a seat is equally safe. An adult belt is designed around an adult body, and on a child it typically sits across the neck and the soft abdomen rather than the shoulder and hips. The exemption is a legal fallback, and booking a proper seat in advance is the option that actually protects your child.