My DD started at the LA pool at age 4. It took around 9 months to get her Level 1 - I put this down to class size (8 sometimes 9 or 10 as children were earmarked to move up a group children in a group with a teacher and a helper). Lots of hanging around and turn taking.
In the stage 2 group, she plateaued as a result of a group of 10 children with 1 teacher and too many "fun" activities that created too much excitement and not enough focus and practice. Again, lots of time waiting for her turn. Inconsistent staff didn't help.
She had 18 months worth of lessons at the LA pool in total and didn't move from level 1, despite having lots of fun.
A place came up with a private swim school and we snapped it up (waiting lists at all possible schools in our area). This is her second term and she is about to get her level 2 award. It is far and away better than the LA set up. The main differences are:
The same teacher every week
5 children in the class max (usually less due to absence)
swimming continually - no waiting for her "turn".
teacher has high expectations of behaviour and effort - she is sensitive to each individual child's confidence levels, but takes no nonsense and expects them to try their best.
teacher has planned on a 10 minute buffer between lessons for identified 1:1 work with children struggling or needing a bit more practice at a particular skill. Will also briefly answer any questions from parents in this time. Her lessons start promptly and she will communicate by text or email if there is no time between lessons. She always responds if you request an update.
using the whole length of the pool shallow and deep end (DD has stopped putting her feet down instinctively when tired/bored since learning in deeper water)
The last 5 - 10 minutes is more fun but still very focussed eg - retrieving objects from the bottom, swimming through an underwater hoop, Jumping in at the deep end, floating competitions etc. so still working on the skills needed for that level.
recent swimmers and non swimmers in the same group - this has spurred my daughter on no end.
Good luck with it!