In our case the builders were happy for the carpets to be fitted the day before completion. It worked for us, but be careful if you go this route to make sure the builders are also happy for you to check the cleanliness of the floors - ours were filthy. Otherwise as has been advised, arrange for the carpets the day after completion, you may find your remover will simply keep your furniture etc in a van, or vans, and charge relatively little extra. Good luck and enjoy your new home.