They can claim a sum. They can claim the profit made from breaching their trademark.
However, if they issue proceedings, any claim for £10,000 or below would be a small claim.
As such they can not claim costs.
So yes, they are entitled to something, but not the full sum claimed.
They would need to show they have suffered a loss.
But you dont need to pay their costs.
Can I clarify anything for you about this today, please?
If not, I would appreciate a 5-star rating for my answer, by clicking the button at the top of the screen. I am not paid for my time unless you rate. If you need anything further I am available for a follow up at no extra cost.