Whilst working on my RR yesterday I noticed just how dusty/ dirty it was

One of the things that attracted me to this car was it's honest look including the engine bay if that makes sense

I don't wanna get it steam as I have heard it causes issues

Can anyone advise the best way to do this?

Many thanks
Neil

The engine bay should be quite hardy and steam cleaning should be ok as long as you have the engine upto temp and NOT running while you do it it should mean that any excess water gets boiled off most components, though i find it better to do it on a very hot day to help aid this and help keep the under bonnet temp very high

You can do a good job by hand spraying the whole engine bay with a degreaser solvent, maybe scrubing a bit with a paint brush on the worst areas and rinsing off with a hose.
If you do this a couple of times it should be clean.
When it's dry spray the whole of the engine bay with WD40, looks good, protects against corrosion and nothing sticks to it for the next time.
I used to clean the engine bay of my Discovery with a pressure washer but not sure I would risk that on a RR.

Pressure Washer from about 2 metres is fine - just don't get to close. From a distance its just a powerful hose. 
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The hard way -

Raid the laundry basket for old clothes for rag
Old toothbrush (for the awkward nooks and crannies)
Air hose or bicycle pump or vacuum cleaner with crevice tool and brush
Small paintbrush
Bucket of hot soapy (detergent) water and small sponge
Degreaser - if needed - e.g. Gunk
WD40 - clean and shiny, and easier to clean next time
If anal, some microfibre cloths
Black Plastic Polish - I get best results with Turtlewax "Black in a Flash"

Remove all the big air intakes, engine covers etc and give a good scrub, especially in the "concertina" sections
Remove engine undertray (if present) to attack things from below

I have a steam cleaner as well, but find this is only good to use after you have removed the heavy soil by hand

Good dollop of elbow grease
Skinny and very long arms (or a cloth on a stick) 

Have "RSW All Comms" in Hampshire - happy to help

Current Combustion Engine Transports:
Range Rover 2002 TD6 HSE Alveston Red, Sand Leather
Audi 2004 Cabriolet Sport 3.0 (Amulet Red)
Mazda Eunos 1990 (Brilliant Red)
MG Midget Mk 1 1962 (undergoing restoration) (to be Nightfire Red)