Common problem. The pump is just leaking out onto the engine.
The two outer body O-ring seals have failed.
The vibration of the engine causes these two O-rings to get flat sided and they leak.
Its a simple job requiring a service kit (readily available from any Rolls Royce part supplier like flying spares in the UK). It contains both the O-rings and a new circlip (as I recall though somebody else will confirm).
Your car is probably an EFI car, so yo may have to remove the inlet duct into the airflow unit, and also disconnect a couple of air pipes to get access.
You need to depressurise the Hydraulic systems (best to do both) by slackening the pressure release screws on the accumulators. Leave them slack for now.
Back on top you need to clamp off the feed-pipe to this pump from the hydraulic reservoir. I used a flexible brake pipe clamp on the rubber hose, but you could easily use a small G-clamp. Make sure you protect the pipe from mechanical damage.
Clean up the general area to remove any muck/dust around the pump to keep it all nice and clean as you dismantle and to stop the ingress of dirt into the system.
Undo and disconnect the two pipes on the pump. One on the top end (the high pressure outlet, and the connection on the side, the low pressure feed.
Remove the circlip with a pair of long nosed pliers (or even the right circlip removing pliers if you have or can find them!).
Look at the body to make sure you can tell which way up it is mounted (it will go on either way up and as I recall my front one is the other way up to the one shown in the acc. picture) and then pull it up and off the pump.
Now all you need to do is carefully remove the two old and 'flat' O-rings from the pump itself (don't scratch the O-ring grooves so use something soft e.g. plastic).
Fit the new O-rings, wipe a little LHM on them and on the body and push it back onto the pump the same way off it came off.
Re-fit the circlip, pipes and anything else you removed for access.
Release the clamp from the hydraulic feed from the reservoir.
Now you need to start the car and let it run for a few minutes to allow the system to prime itself and for the air you introduced during the process to be removed.
You can now close the pressure relief screws on the accumulators and then the system should pressurise normally (the brakes will work and the suspension rises) as the engine runs.
You are now finished. Take the car for a spin round the block then get yourself a beer and clean up that oily patch on the path as it will stop growing now you fixed the leak.
Oh, you should top up the LHM reservoir as well whilst you are at it (though if you have clamped off the reservoir feed pipe to the pump OK, you should only have lost a shot-glass full of fluid.
By the way, you should read the manual if you have one.
I have paraphrased it, added my own experience and told you this without any endorsement that this is how the nice people at the dealership would do it.
All I can say is that it was an easy job to do and complete within the hour.