I live in rented accomadation in the west of london but we have a lovely big garden - the landlord isn't too bothered about its upkeep but myself and my flatmates have been trying to keep it under control as its good for bbq's

We seem to be losing half our lawn to the below plant - its in a position that catches the sun at certain times of day but is overshaded by some large trees. The soil seems quite dry but I'm not sure what kind of soil it would be (not really a very clued up gardener)
we cut this plant back and do our best to get rid of as many roots as we can pull up but it's worse4 than dandelions, the roots all seem interconnected and are pretty tough - they may even have some kind of tuber on them - or i might have pulled up something else...

anyway three photos below of the leaves and flower on the plant - can anyone tell me what it is so I can find the best way to deal with it??

Many thanks

(incase the pics don't work - the plant is maybe ten cm tops, with big round leaves (green) - sort of like a filled in horseshoe shape with just a little triangle missing from the shape where it connects to the stem, the flowers almost look a little thistle like but soft - sort of like a closed up dandelion flower - purpleish. )


unidentified weed

unidentified weed (pic 2)

unidentified weed (pic 3)