In the past I've bought and sold using a CHAPS transfer and cash and both were hassle free.
With the CHAPS all we did was go into the bank of the buyer and request the transfer. When you're with the same bank it happens instantly. With different banks, as long as you request it before lunchtime-ish (varies by bank up to about 2pm) it'll be in the same day.
What I've done with cash is take the buyer to my bank. Never touched the money myself and asked him to hand it over. Maybe being paranoid but it was a tip I was given incase the money was dodgy or there was a shortfall. With one car the buyer just added a couple of grand to the cash he'd recieved for his previous car which must have been over by about £20. Unfortunatley the teller noticed and he got it back
I'd never pay with cash but I would accept it as long as the bank was open. CHAPS would be my preference though. The only problem you've got is if you do the deal on a Saturday afternoon or a Sunday when the banks are closed......