clover

I killed all my "Non grass" in March / April with a couple of applications of Weed n Feed. Not top brand stuff either, I used a cheaper alternative from BnQ.
If you get regular rain, it may be worth a try now. Or, if you have the luxury of unmetered water/no hosepipe ban you could water it in.

My lawn is nearly all brown now, no decent rain for 5 weeks. I cut it too short last time too (Mower now altered).

If you have more clover than grass to spray out the clover will just de-nude the lawn. I would tolerate the clover, as it is green stands drought and it cut regularly is no problem.But if you want the perfect lawn kill the whole thing and start again.Most people cut lawns too short, half inch is short enough unless you want putting surface!!!