On new cars, a franchised Audi dealer will 90% of the time use Audi Finance (VWFS), simply because of any finance incentives/deposit contributions/subsidised rates offered for the various models as part of each quarterly sales campaign by the manufacturer - these are then used alongside any dealer discounting of the car price to get you the deals you all want on new cars.
There may also be some reactive/impulse deals available from time to time for dealers to use to help sales (eg, 0% interest on a particular model for a limited time, etc)
It would make no sense to go to the likes of Blackhorse or other funders for new cars as Audi Finance will be offering the 'best deals' in general - the dealer in return receives a flat documentation fee/commission for each finance deal struck, which may differ from model to model - it may be something like £400 commission per car sold on finance, so not a huge earner for the dealership (many new cars are sold at a loss/minor profit in order to sell the unit - the biggest earner for a dealership is a volume bonus paid by the manufacturer for hitting set sales targets on overall units sold per quarter/year, etc)
However, let's say a customer is declined by VWFS for perhaps a poor credit record, affordability reasons, or VWFS simply deem that customer to be too high risk...a dealer is free to seek out any other finance provider (but who will not provide the large customer incentives/contributions offered by VWFS) - but their franchise agreement with Audi will have a clause to say that VWFS are to be offered each finance case first.
Used cars is a different ball game, as in general, the interest rates offered by VWFS (or any other lender used) will be unsubsidised so tend to be anywhere from 7% to 12% (but may offer 2 years servicing, extended warranty, etc) as part of those rates. The dealer is not lending the money - they are simply acting as a credit broker.
A franchised dealer will generally have some flexibility to reduce used car rates from the structure set out to them by VWFS (if they want to - depending on the economics of the whole transaction, they may have more profit in the actual car itself so can sacrifice a little commission, or the car may be losing them money, so will be seeking to recoup as much as they can from finance commission ), as VWFS will be paying them a commission based on the overall finance profit - if the dealer sells a car at a higher rate (hence more profit for VWFS), they will receive a higher commission
Some finance companies will have restrictions of the type of used cars they finance, depending on age, mileage, condition, etc - some may have a maximum age of car for PCP, or mileage, or anything that perhaps restricts finance availability
For this reason, franchised dealers will generally have 2-3 main prime lenders they use for used cars (VWFS, Blackhorse, plus several other large finance providers) and will also likely have a source of funding available for "sub-prime" borrowers for poorer credit records that can still buy a car, but have some type of blemished credit record - APR of 18% plus would not be uncommon for these type of borrowers as they are higher risk
For the record, dealers do not set the guaranteed future value of a new or used car on PCP - that is set by each finance company depending on age, mileage, usage, spec, etc as it is the finance company that is underwriting what they believe the future value to be - two different finance companies could offer the same APR on the same car, with the same mileage and up front deposit, but depending on what they estimate the future value to be, it could have significantly different monthly repayments