How can I prevent water seeping up into my carpet?
I'm guessing you're in the UK, right? If so, the cause is probably rising damp. Likely your cottage has no damp-proof course between the foundation and the floor and walls. So moisture is simply constantly trying to push its way into your house.

The true solution is to radically improve the waterproofing and drainage of the cottage. This is probably not a DIY job; you'll need to hire professionals. In the UK there are a lot of people who can do this kind of work.

A cheaper solution would be to remove the carpet (bad choice for a non-waterproofed foundation in a wet and rainy climate) and replace it with something that's immune to the effects of moisture, like ceramic tile or stone. But damp-proofing the foundation is really the right solution.