I think you are over estimating the quality of school swimming lessons
This.
Despite you telling us you 'learned to swim' solely through lessons at your school back in the day, OP, that really isn't the case for 99% of children, or schools for tha tmatter.
Learning to swim takes at least 2 or 3 years of regular lessons to build confidence, stamina, different skills. I'd consider it an 'essential' part of child rearing costs, and something that should be factored into the cost of bringing up a child as much as paying for nursery, after school club, holiday clubs etc is. Learning to swim could save your child's life one day - and a term learning at school haphazardly with a whole class will not achieve that level of skill.
My DCs went to swimming lessons from the age of 3 (I didn't do 'baby swimming - that's not really essential when it comes down to it, and I couldn't afford it) and they stopped at around Year 4/5. It did cost a lot. We lived on a set amount of cash for several years when they were small, no holidays, no meals out, no 'extras' of any kind other than what was essential to keep them safe before/after school when we were at work, but swimming lessons were part of that. There's no way they'd have learned to swim in a term, or even a whole academic year, at Year 5 or whatever. That's far too late.
So because money was short, DC didn't do any other kind of paid activity when they were small, other than Beavers/Cubs (nominal subs) and swimming lessons during those few key years.
OP, this is really down to you to sort out, not the school. My DC also had no lessons at school because it wasn't offered back then.
You should have started them years ago with a swimming class - at around ages 3/4. If you had, you wouldn't be where you are now (harsh, I know, but true). As I say, you have to prioritise swimming as a 'life skill' - it's not in the same league as dance classes, or gymnastics or learning to ride a horse - they're luxuries, nice if you can afford them (we couldn't). But swimming is important. You can't pass that responsibiity onto others now, OP - it was alway your responsibility to sort out. (Again, harsh but true - sorry). 