welcome to GOY.
you should be able to buy broom in the garden centre.

when you say thistles do you have any in mind? ie Native ones or cultivated garden ones?

If you want wild ones then you should be able to get seed.
But don't dig any up from the wild as that is illegal. Though taking a little seed is ok.

If you collect wild seed be careful about the variety -some are much more attractive than others. Think twice before them in your garden though - they will seed around with enthusiasm.

Did you mean Cirsium vulgare as a cultivated thistle? Or Cardoon Cynara cardunculus?