Motorcycle passengers, otherwise known as Pillion Passengers whether on a moped or motorcycle, represent a fairly small number of casualties, but their injuries are likely to be severe.

Pillions and riders are likely to have similar protection to the upper body in terms of jackets and helmets, but are probably less likely to have motorcycle boots, gloves, jeans or any sort of body armour. This means the risk of serious injury is greater. You should do everything you can to minimise the risk of injury.

Only motorcyclists who have passed a motorcycle test can carry passengers. (Regulation 16 of the Motor Vehicles (Driving Licences) Regulations 1999.)
 
The machine must be equipped with suitable supports or rests for the feet of the pillion passenger. (Regulation 102 of the Road Vehicles (Construction and Use) Regulations 1986.)

Pillion passengers must be capable of sitting astride a proper seat securely fixed to the motorcycle. This may require specific adaptations to accommodate young children. (Section 23(2) of the Road Traffic Act 1988.)

A pillion passenger must wear a safety helmet. (Motor Cycles (Protective Helmets) Regulations 1998.)

The decision to carry a passenger on a motorcycle remains with the rider, who is legally responsible for ensuring that the passenger is safely supported. (Section 23(3) of the Road Traffic Act 1988.)

Any passenger must be carried in a manner so that no danger is caused, or likely to be caused, to any person on the vehicle or on the road. (Regulation 100 of the Road Vehicles (Construction and Use) Regulations 1986.)

It is an offence to use a vehicle when the number of passengers, or the manner in which they are carried, is such that it involves a danger of injury to any person. (Section 8 of the Road Traffic Act 1991) 

You could also, as well as following the legislation, ensure you:

• Align your body with that of the rider.
• Grip the grabrail, or hold the rider at the waist and grip with your knees when braking.
• Pick a shoulder to look over and don't change shoulder or wriggle about when cornering or braking, although this may be fine at other times.
• Stay still as the motorcycle is coming to a stop, to aid the rider's ability to maintain the balance of the machine.
• Keep your feet on the footpegs at all times.
• Make sure the rider is experienced and aware of the difference having a pillion passenger will make.

These things may help but despite your best efforts it is unlikely to be your fault if you are involved in an accident. It is far more likely to be the fault of the rider or the driver of another vehicle. You, like the passenger in a car, will be an innocent passenger. You do not need to worry if you are related to or close friends with the rider of the motorcycle or moped as the claim will be dealt with by their insurers.