There are two types of invasive thistles in Britain - spear and creeping.
Creeping thistle will eventually respond to repeated mowing or grazing right down. We've not tried weedkiller with them.
Spear thistles need to be dealt with by hand. The only way to remove them completely is to dig them right out, one by one. The most efficient way to do that is to make a T shape at the stem with a sharp spade, then ease out the entire root in a one-er, which barely leaves a hole behind. The spade goes in vertically on one side of the plant, the 'stem' of the 'T' is at right angles to the thistle, on the opposite side. This is done at this time of year, when the flower stem is up but the flower hasn't opened. Too soon and they grow back but multistemmed, later and the seeds have blown everywhere. There's no need to use any chemicals at all.
We know this because we've tried everything, except weed killer because we'd rather disappear in a sea of thistles than pour chemicals on our land. Anyway, if you use chemicals to kill the plants, you still have to collect and dispose of the dead material, otherwise it sticks to you and your livestock and gets caught in the hay
When we first realised we had a problem, we just about had disappeared under a sea of the things. We kept getting the timing wrong - because of course there's plenty of other stuff going on right now. Eventually we paid our eldest grandson to remove every thistle from 4 paddocks, totalling about 5 acres. he did quite a good job, and the following year there were far fewer to contend with. Each year we dug them out and built a huge funeral pyre for them. This year, there were only 2 wheelbarrow loads, so a funeral pyre for a mouse. So it takes a few years of work, but you can get there in the end.
It's so important not to let them seed that we sometimes extend our digging onto our neighbour's land to get an odd one. Just that one can reseed your entire holding for the next several years.