We left one half of ours for May and June last year and honestly it looked awful and was a bugger to cut when we did do it. Also we got wet ankles going up and down to the greenhouse in the mornings because of the dew. The cats clearly didn't like it either.
This year I have only done it once so far (at the end of March) and I went carefully around all the areas with flowers - we get lots of primroses, speedwell and dandelions but they tend to stick round the edges not cover the entire lawn. I am going to leave the parts with these flowers for a few more weeks but the main part of the lawn is getting cut.