Viola for sure. Lawn weedkiller is the only way. The roots are persistent so any bits of them you leave behind will regrow. They also can go straight from bud to seed without flowering and the seed pods explode and send the seeds scattering. Almost impossible to eradicate. Sorry.

I wouldn't hesitate to use a lawn weed killer. You will probably have to do it several times during the next year. The secret will be not to let them flower and to carry on hand weeding the odd ones. I bought some to put in the rockery in my front garden at my previous house and the wind blew the seeds from the old flower heads right across the road to the opposite front gardens.

Thanks guys. Will get my lawn killer and spray out and have a go! Think it will be a long process......

There is a weedkiller with an application head that produces a foam which will stick only to the weed leaves that you want to eradicate for precise spot elimination and to lessen collateral damage. I have been using it for tight spots and it works great.

Owdboggy tells of violas going directly from bud to seed. Some have the abilty to self pollinate within the bud and this seems to happen more on the second flowering of the season. These violas are said to be 'cleistogamous'.
Sorry for going off-topic on your post Amsterdam but this is a word that I have just learned and I am showing it off! It came about because I have some Viola jooi, in pots, doing just this.
To get back to the original question I would also think that a suitable weedkiller is the only solution.

Loosestife -any idea what that particular weed killer is called? I get rather befuddled in the store faced with a huge selection of weed killers....
Bulbaholic- we learn something new every day! I had no idea that could even happen. That explains why it spreads so easily....

I'm pulling these out of a front border all the time. And to think how thrilled I used to be to find a few dog violets...

I knew the word 'cleistogamous' but I did not want to show off! (Huge grin).
We use Weedol Lawn Weed Killer. It seems to work.

What a great word Owdboggy! Just looked up the derivation to help me remember it. (apparently means closed mating")

Ams it's Roundup. Some of the bottles come with spray or stream and some come with spray or foam application.

Be careful using Roundup or glyphosate - it also kills grass. Otherwise, for lawn weedkillers, check the bottle to see if it mentions wild violets as one of the things it kills. More effective treated in autumn,but repeat treatments next year will likely be necessary.

If you don't want to keep treating the grass; which I believe you should only do a certain number to times in a year, why not use a weedkilling gel or add some wallpaper paste to glyphosate and paint the little devils in between treatments? Might be easier than digging holes all over the lawn.

Thank you all for your rep,ies. I will start to tackle them one by one with a concoction of foam or a gel.