Paying with cash won't necessarily enable you to negotiate a lower price, but it will save you paying lots of interest.
Once upon a time, cash was king when it came to buying cars, but that's not always the case now. If the dealer is struggling, and you insist on paying cash, then it's a case of 'any port in a storm'. But realistically they make so much money from finance agreements, that's where all the savings are to be had. Not by offering large discounts to cash buyers. I'd do what Fred suggests, make them a sensible offer that you're comfortable with. Or ask if there are any deposit contributions available for taking out finance, then sign up and pay off straight away.