I bought a light carpet a few days ago and it got fitted today. I
noticed a couple of relatively small marks on it as it was being
fitted, but because it was reminent and I got a reasonably good deal
on it (£170), I thought I would just be able to clean it. However,
after the fitter had gone, and under a different light, I noticed
loads of other marks that appear to have been made from his shoes.
Now the whole carpet looks dirty and ruined, and needs a professional
clean.

What's my situation here? Can I claim the cleaning costs, and from
the fitter or the shop?

Did you get the fitter to lay the carpet, or was it all dealt wit by the
shop you bought it from?

If you paid all the money to the shop, then it will be down to the shop,
irrespective of whether it was already on the carpet before fitting, or the
fitter damaged it.
If you bought the carpet and got a fitter to lay it independently, then you
need to make sure you accuse the correct person!

Sparks...