Any lawn care experts here? My front lawn is a mess :(

Hi all! I can't tell you how useful this forum is for me at the moment. I am sorry if i don't always reply, I have 4 kids self isolating at home and work from home too. Gardening is the only thing that's keeping me vaguely sane. I think it's about time that I sorted out my front lawn. It appears to have been taken over by whatever this is and it feels like an absolutel neverending thankless job. Where do I even start? Picture to follow ------->
Growing a pink garden, one plant at a time....
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If you run the mower over it, that will get rid of the flowers and straight away it will appear greener. If there is a drought you will find the clover is the only green left while the grass turns straw coloured.
You can apply weedkiller if you really want to, although with children around you'll need to keep them off the lawn for at least 24 hours.
To be honest, with everything else you've got going on, l would just put the mower over it and it will instantly look better.
Unless you're aiming for bowling green standard l wouldn't stress about it too much (just don't tell my husband l said that)
https://www.rhs.org.uk/advice/profile?PID=357
Something like this
https://www.amazon.co.uk/Resolva-Killer-Extra-Ready-Litre/dp/B00PLYYR8G
Sprayed on a muggy, still day should start to put a dent in things.
I guess the issue is if the clover is so well established, you kill it and end up with bare patches and need to re turf or reseed!