It depends on their age and the airline - it's best to check the airline policy to be on the safe side - my nephew was just over 16 and he required one.
noone needs a passport to fly internally in UK or between UK and Rep Ireland.
You will need some form of photo ID though - check with individual airline as to what is acceptable
Photo-Id for children under 16 years is not required in the following circumstances:
o Children travelling with an adult on UK domestic flights and UK-Republic of Ireland-UK routes.