Do pre-approvals affect your credit score?

In short, no they will not, they are different to a credit card or personal loan application. It will be recorded on your credit file as an enquiry though showing the lender, amount requested and date you applied.

However, if you make many enquiries with multiple lenders in a short time, this could affect your credit score as it could look to a lender that your loan has been declined and they may not want to lend to you.