A soft credit check won't affect your credit score.
Future Finance will still be able to see all the information required to check your eligibility to proceed with your application. The record of this search is only visible to you and Future Finance. If you check your credit history with one of the UK's credit reference agencies, the search may be recorded in your credit report but it is only available to you.
Other companies will not have access to this information should they complete a credit search on you so it cannot impact their decision making.