WLSD,
I can absolutely see this one from both sides - as a parent and as a teacher.
From the 'teacher' point of view, the school "per capita budget which would include money to take children swimming" [there's no dedicated money] does not vary depending on whether you are a small rural school 10 miles from the nearest pool, who takes say 40 children at maximum because of the size of the school, or a large urban primary round the corner from the school, who take 60 children swimming at a time.
However the actual 'cost per child' of taking the children swimming is hugely different in the two cases. There will be a fixed cost to hire the pool and a fixed cost to hire any specific instructors - per capita cost much higher for the small school. The urban school will have no transport costs, the rural school much higher.
It is then a question of priorities for the rural school - who also have much higher costs for most trips etc as well. Is swimming offered to all for free? Or is a voluntary contribution invited so that there is some budget left for other items? The large urban school is in a very different position. The heads of each school will balance a whole host of different priorities and have to make a judgement about where voluntary contributions are requested and the consequences elsewhere if swimming is a huge drain on reseources.
Yes, your taxes pay - but they pay the same amount per capita to the two schools, while swimming is a much greater drain on the resources of one than the other. That is the dilemma schools face.
Voluntary contributions can be invited. Families on FSM should have it made absolutely clear that the provision is free to them. And all possible steps should be taken to reduce costs while delivering quality swimming lessons.