Bought 2003 Cooper S a couple of months ago and have water/coolant loss.....if I drive at under 3k revs all OK but if above I need a litre after 50 miles.

In last 12 months its had:-

New Radiator
New Header Tank

In last 1 month:-

New Thermostat

Main Dealer has done a pressure test and I've also tested for combustion gasses in header tank and looked all around and cannot find the cause.

Any ideas???

Is the pressure cap ok? Cheap and easy to replace and they can cause very similar problems without being very obvious to see when faulty.
Also has system been bled of all air?
More:
Solving MINI Cooling Problems.......... - Forums (http://forum.minicooper.org/showthread.php?t=13263)

could be the water pump!

We had boiling problems with coolant loss, boiled when my missus was driving it, checked everything for leaks, suspected head gasket had blown-with luck it hadn't.
When underneath the car I noticed anti-freeze staining where bottom radiator hose is attached to radiator, when I flexed the joint by hand water poured out, it appears that over time and heat, the plastic coupling which houses an o ring seal distorts and leaks water even though the flange is bolted to the radiator.The leaking water is hard to notice because it runs inside the plastic trim under the rad.
I pulled it loose, which is fiddly and as a temporary job, put two large washers over the bolts to pull the distortion in the fitting out , whacked the joint with sealant an re-fitted. It has worked for a while but is leaking again, so I need a new part, apparently they do not sell this part on its own-you have to buy a complete rad at £120.00. I have noticed that on some forums leaking radiators are cited as a common fault on Mini Coopers & Ones, just wondering if its this part that is at fault, they should sell this part individually as its totally detachable from the rad and bottom hose , the distortion is caused by poor material , nearly cost me my engine,I am going to have a mate knock one up out of steel plate & pipe because I am tight .
I had to bleed the water after re- filling as the system had an air lock, the header tank was full but there was a void in the pipework.

The bottom rad leak is common on earlier Mini's and as said the official fix from Mini Dealers is complete replacement with the new 'improved' design radiator.

I assume all the hoses are in good condition? are they the originals?
Sometimes a hose can partially collapse internally whilst still looking ok on the outside if its an old one, if one has this would restrict the coolant flow at higher revs, similar to a blockage and cause high water temperature and hence overflow.

I bet it the alloy fitting on the block where the water pump fits in to.

You have 2 o rings holding water there.

we normally charge 3 hours labour to fix.