It was only KS1 pupils who were entitled to FSM, KS2 had to pay or take a packed lunch, just to clarify.
The point is who is going to pay for supervision of Breakfast Clubs? It's not the case that most schools already have them either. When I worked for the LEA I provided funding for setting up Breakfast Clubs, to pay mainly for equipment such as large toasters, a fridge, dishes, cutlery etc. In schools who didn't have their own kitchen. But the ongoing staffing costs were picked up by the school as they had a budget for Out of Hours provision, which has since dried up.
It can't be right to take away a cooked school dinner for 'infants' and replace it with a bowl of cereal, a piece of toast and a glass of juice.
Incidentally my GC attend 3 different schools and none of them run a Breakfast Club.