I use 'Weedol - Lawn Weedkiller' once a year on the grass. <<Edited
I find it keeps the numbers of all weeds in lawn down for the whole year after application using a watering can.
And I then remove any others by hand before they get too big. https://www.amazon.co.uk/Weedol-litre-Killer-Concentrate-Liquid
For those in the image, pull them out now, and let grass grow where the holes are.
Keep pulling them out before they get too big and kill the grass under their leaves.
Use a Stanley knife to get under those weeds in the picture -- if you push it in under the weed you can 'pop' them out by cutting the tap root. Can take a while but it's the most effective way.
As for future treatment a good weed and feed will do the job, although it'll take a few applications over the course of a year to yield good results.
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