It is a myth that a previous occupier of your address can affect your credit rating. Credit search is based on name, DOB, address and previous addresses. Unless a previous tenant of your address had the same name and DOB as you, then it has absolutely no bearing on your credit score.
It is true that it can be problematic if your new address does not show up on the postcode databse yet. If you have this problem, get in contact with the Post Office ASAP and first of all, make sure you have the correct postcode for your address, and secondly, make sure your newly built address is added to the database. Most banks will ask for additional proof of address if they cannot verify your address on the postcode database.
One caveat I would add to my first statement, one of the banks I used to work for would automatically reject credit requests from a certain postcode in the UK. This was a very special case. There had basically been thousands of credit card and loan applications from this "address", some had been approved, all were fraudulent. It turns out the street which the postcode referred to wasn't a residential street, and there was systematic and organised fraud being perpetrated by a criminal gang from this area (it was in Birmingham). That was truly a unique case, where any application for credit from that postcode was automatically refused. I could forsee problems if at some point in the future, there was a bona fide residential address at that postcode.