InWith has clearly explained the obligation of schools to provide a 'varied menu of activities'. Both free and paid-for activities fit in with that.
However, as an ex-senior leader in a primary school I find some of the moaning on this thread very depressing.
I went to primary school between 1979 and 1986. Two primary schools in different areas of the country, but both in pleasant, fairly well-to-do areas.
Were there any clubs on offer? No. Nothing. We received very, very little in terms of curriculum enrichment. Perhaps the occasional trip. The most exciting thing that ever happened in my first school was that one year we got a new headteacher who decided to put on a school production, with proper stage lights! The schooling experience of children attending primary school nowdays is hugely enriched by the 'offer' of a wide variety of opportunities.
Teachers are not obliged under the terms of their contract to offer extra-curricular clubs, however many do. I have done so twice, once on a voluntary but paid-for basis (no other member of staff was running a club at that time) and once as a requirement from that school. However, the workload of the average primary teacher is pretty significant (I have generally worked 55 - 60 hours a week) and it is a big drain to give up that period of time after school when you could otherwise be sitting down in a quiet classroom to get on with planning, marking and all the other tasks required of you. It is also unlikely that the workforce of a primary school will be able to supply all the skills in gym, dance, capoeira etc that clubs might demand.
No school I have worked in has received 'kick backs' for distributing leaflets. Indeed, I am aware that the school office or head has often filtered out and binned the truly unsuitable offerings.
Moreover, the facilitiation of such a club runnning on school premises does involve work and effort on behalf of the headteacher. Fielding the phone call, meeting with the representative to find out exactly what they are offering, checking for valid CRBs etc, explaining that yes, you do have to make sure each child is collected by an adult at the end of the club.... If the school is also doing the 'wraparound' by helping the club to collect the children from each class, so they don't have to be collected by their parents and looked after during the gap, then that is positively helpful to working parents or those with other commitments. My last school actually had to employ somebody especially to handle the process of collecting/dropping off to after school clubs, because all staff would, quite rightly, be busy in their classrooms at the end of the day.
So, YAB pretty U.
I suggest that you speak to your Headteacher and ask if the PTA can set up a bursary fund for after-school clubs.