I know this might sound like a ball buster, but I'd recommend selling the Mk5 privately. Dealers have this unerring way of only giving you around half what the car is actually worth. By selling privately, you will be reducing the total amount of the £22k you were planning on spending (obviously).
Secondly, make a point of going round 2 or 3 garages & asking the question / making the statement ...
" I'm looking for a Mk7 Golf & want to pay cash, how much of a discount off the retail price will you give me ?"
I can bet that most will say (with a straight face), "just what the ticket price states, sir..."
(NEVER accept that answer ! Advertised prices can always be tweaked down / argued over)
That aside, if you get a couple of them to 'quote' you a price, play them off each other by stating that Garage X will sell me one for Y pounds, can you match or better that ?
Yes it's a lot of donkey work & running around, but if you get said £22k car for £18.5k & you sell your Mk5 for £3k, you've technically bought a £22k car for £15,5k !!
It's worth a thought !