The Volkswagen Golf VII can be had with ACC, so a 2.0 TDI 150 6-speed wet clutch DSG might meet your requirements. Early Golf ACC had problems, sometimes stopping the car dead for no reason, but they seem to have got it sorted out by now. The latest Volvo ACC works down to a standstill and will even crawl the car along at a fixed distance in traffic jams, but I don't think you can get it for £25,000 new or used. Ford ACC in a Focus 2.0 TDCi Powershift stops the car dead, and so does the ACC in a Mazda 6 from 2015 (I've filmed myself stepping out in front of both of them and I'm still here). Honda CR-Vs have had ACC for a long time, back to 2006, but it doesn't stop the car entirely.

For quietness and comfort, go for 16-inch wheels with 205/55 R16 tyres and change them to Michelin Cross Climate as soon as they wear out. 17-inch and 18-inch wheels and tyres will not be as pleasant.