Edit: Sorry, misread your flag! No offense intended, honest! Post removed.

In my case it wasn't oil, but as it apeared - particles from exhaust system. The egr valve cooler was invalid and allowed some black stuff into cooling system.

Hello,

I'm probably too late, but you need to be extremely cautious here. All vehicles these days with auto boxes have a separate system within the engine cooling radiator, with pipework running from the gearbox. The reason for this is that the auto box will reach working temperature quickly - with help from the higher engine radiator temperature during the vehicles cold starting on frosty or cold days.This reduces emissions from the vehicle, the ultimate objective.

Mercedes had a huge number of radiator failures - The C class was one example, when their French supplier "Valeo" supplied substandard systems. The effect was to contaminate the auto transmission oil with water and cause the transmission to fail catastrophically. Toadshall

I had the same problem as the OP.
The Oil Cooler was leaking oil into the water.
Had the cooler replaced by my LR dealer.
3 hours of work. Costed 460 euro's.
On the old cooler there was nothing visibly wrong, must be inside of the part.

The oil cooler is a pretty common fault on the ford engines.. I have had 2 go when my guys haven't put on the heater on during the night. It's a cheap fix, but it is a pain trying to sell a car with a black expansion tank, you will never really get it clean. Same symptoms for us, black oil, but its water underneath in the expansion tank, it looks much worse than it is.

A 460 euro fix ain't cheap imo