You've done all you can as a DIY car inspector. The paperwork checks out, the car drives OK, and you discovered no faults that can't be put right if you get the car at the right price.
If you feel confident about the car, go to DOING THE DEAL. But don't forget that we recommend a data check on the car if you're buying privately. It's a small price to pay for peace of mind.
If you like the car but feel you might have missed something, ask yourself whether it's worth spending £100+ on a professional car inspection . Don't forget that if the inspection reveals minor faults, you can use these to negotiate a lower price. And if it shows up faults serious enough for you to reject the car, you've saved yourself money and heartache in the long run.