Welcome to the forum Melissa.
Not an expert on creeping thistle, but I understand that, if control is by cutting, they need to be cut close to the ground (below all leaf growth) and repeatedly for a long time!! (Any plant root system that is "starved" by repeat cutting of vegetative growth will eventually expire.)
Also, for chemical control on anything other than a domestic garden, you now need a certificate to apply "pesticide/herbicide" (the training/certificate costs somewhere around £400 at last check) or otherwise use a certified contractor.
Nimbusllama mentioned selective weed-killer: of course, a non-selective glyphosate based weed-killer will do the trick by applying to individual thistle growth. Spot spraying over some 4 acres is, I would suggest, viable unless you are really struggling to find time for everything else that you want to be doing.