This is viewable (pdf) here.
The total number surveyed by Research First via telephone was 806 over 4 quarters. Despite that small sample size, they seem reasonably confident of the accuracy (there is a margin of error of 3.5%).
Libraries got the highest satisfaction level at 96% and — unsurprisingly — “value for money” one of the lowest at only 41%
Its fairly easy to ask patsy questions. Like “Are you happy with the current level of rates increases” obviously wasn’t asked.