Intermediate level airbrush and compressors for <=£250 (approx $400).

My wife was thoughtful enough to buy me a compressor for my birthday. It was a Taiwanese Grex model that she picked out because it is fairly quiet. Not my choice because it didn't have a tank but I guess the thought counts. I actually made my own small ( less than a liter in volume) tank for it using plumbing parts. The compressor does seem to be very well made, can put out up to 60 psi and will run for very long sessions. It was about $200 USD, plus whatever I spent on my do it yourself tank.

Samulus

The compressor needs to be:

3 - function for at least an hour without cool-down time.

4 - It needs to be of the type where you can set a pressure, say 30psi, and then it fills the tank and turns off, coming on again when you've been spraying for a while and the tank pressure has dropped enough. 

These are very tall order for an under £250 compressor, much more so for a complete system. "Functioning for an hour" is easier than running the compressor motor continuously for an hour. Recommendation is to get a twin piston compressor from Taiwan. Avoid the made-in-China compressor which runs a lot hotter.

Since you did not mention how often the compressor can turn on again, so any size airtank can do.

The cheapest match is the £200 Revell Master Class Compressor. You can get a Neo for Iwata for £50.

Good luck and let us know what you find for £250.

You choice of compressor, or rather the origination of the compressor will have a noted effect on the overall costs - you can get a made in China airbrushing compressor to meet your  needs for less than £100, but if you want to move up the ladder (quality & longevity wise) & get something of better quality, you are looking around £180.

With the cheaper compressor, this leaves the door open for an excellent choice of airbrushes, such as the H&S Evolution Silverline 2in1 or Iwata Eclipse (even Kustom Eclipse).

Going for the dearer compressor will leave you with the likes of the Neo for Iwata or H&S Ultra.

Bringing the budget up ever so slightly would get you a tanked Sparmax compressor & something along the lines of the Iwata Revolution or H&S Evolution/H&S Evolution Silverline, which is pretty much all you may ever need.

I think airbrushes are a lot like cameras.  Some folks are very strident on preferring a given brand, but when I average all the recommendations out, I think any of the major brands do a fine job, else they would have not stayed in business.

BTW, as far as pulsing.  My current compressor does not have a tank, and hence does have a rapid pulsation. I was a little leary about this, but find it does not have an effect on my finishes.  The pulses are so rapid they are swamped by the movements of the brush and buildup of paint.  I also do notice a drop in pressure from trigger actuation and this I DO find a bit objectionable.