Gone are the days, Julie, where a dealer would discount a car for a cash payment because of strict rules on the amount of physical cash a dealer can take before informing Inland Revenue and Customs that you are using cash (money launderers beware). The dealer would knock, say £500 off for cash (knowing he could knock off £1000) and pocket some untraceable cash as well as his commission.
This doesn't happen nowadays, especially at a main dealer. If anything, you would get a discount for using Finance as Dealers earn commisson from the finance company for each agreement paid.
This isn't to say you shouldn't get a discount anyway. It's up to you to negotiate a discount though. Tip, if anyone asks me for a discount for cash, I explain as paragraph one and hope that the customer accepts this, quite often they do, often though I end up doing some discount or other to close a deal.
If you think there is more discount to be had, you have to ask for it. Don't expect it to be for cash though...
Jon