The typical price gap
Private sale prices on Autotrader/Motors tend to run £500-£1,500 above the average dealer part-exchange offer for the same car. On lower-value cars (£3-£7k) it's less; on higher-value (£15k+) it's more.
The time cost of private sale
Realistically: 3-6 hours of listing, photography and messaging, plus 2-6 hours dealing with viewers, test drives and eventual sale. On a £5,000 car that's often £150-£250 per hour of your time — a decent rate.
The middle-ground option: car-buying services
Motorway, We Buy Any Car, Cazoo etc. sit between the two. Prices typically £200-£800 below private sale but £300-£800 above dealer part-ex. Collection is next-day. For most people, this is the best value-per-hour route.
When part-ex genuinely wins
Cars with issues (MOT close to expiry, high mileage, cosmetic damage) sell far better through part-ex than privately. And if your current car is on finance, the dealer can settle it directly rather than you needing to bridge the gap in cash.