Buttercups taking over HELP!!

I live in bude, Cornwall SW England.
We have a few acres and we have a couple of horses.
Our problem is that creeping buttercup takes over in the summer and the horses will not eat buttercups I have heard they are poisonous to most grazers, so I'm looking for a permaculture approaxh to get rid of the buttercups without the traditional method of plowing and liming the fields.

Would appreciate and experience or help.

Joe

I've beaten it in small areas using wood chip mulch - the roots only bind loosely, so they become easy to pull up. This works great in cultivated beds and around fruit trees, but not really viable on the scale of a pasture.

Patrick Whitefield's book The Living Landscape suggests that the reason buttercups tend to take over is because animals graze around them, giving them an unfair advantage. He has controlled them by regular mowing, which removes that advantage.