The £4000 mark is a minefield. It is too much to loose on a POS and too little to be guaranteed a bargain.
It is true that fantastic cars can be had for £4000 though.
I once bought a 1 previous owner golf, low miles at around this price point, It was eventually a very good car after I had sorted it out. I paid to have a scratch painted on the boot, then the clutch went (depends on how they have been driven) then I had to do the brakes, the cambelt, the tyres and then the exhaust. All of a sudden that bargain £4000 car wasn't so much of a bargain.
It was fine after all that had been done though.
A friend of mine has just bought a '51 Ford Focus estate (for work) 60,000 miles, 2 owners 1.8 TDCI for £1500! At that price I could stomach a few repair bills such as tyres and exhausts.