Swimming lessons start from 3 months. Around aged 2.5 is when they go to lessons independent from their parents.

Im a swim instructor and we are taught that floaties interfere with children learning how to float independently and keep their bodies up when swimming.
Its interesting you say that, we're we take our 2 swimming, DD wears floaties for the main part of the lesson (she's with 1 instructor to 3 kids), and DS, who goes in with DH, wears them for a little bit. When the instructor is giving them one on one time, she takes them off. I didn't think it was hindering DD's ability to swim at all, but then I haven't seen a child learn to swim without them.

I do like the floaties though, as it gives us that extra bit of security, we're always in the pool with her or next to her in the sea, but I always thought it gave her a bit more independence.