what is the best product to clean and remove the grime from the chrome exhaust

Autosol is far better than anything I've used, it'll do what you want it to!
 
what material are you useing to remove it, microfibre cloth?
 
Exhaust Tailpipe
Two things that can ruin the freshly detailed look of a vehicle; dirty glass or exhaust tips; the exhaust tips can sometimes make or break the rear view of an otherwise pristine vehicle. Spray down the inside and outside of the tips with P21S® Total Auto Wash or P21S® Polishing Soap, allow to to remain in place, it will to start break down the grime. To clean the outside parts of the exhaust use either a Mini E-Z Detail brush (they are perfect for cleaning the areas between dual-tips) or an old micro fibre used strictly for dirty jobs and Optimum Metal Polish.
Use #0000 synthetic steel or bronze wool (very fine grade) with P21S® Total Auto Wash to clean out the insides of the exhaust tips. Polish using P21S® Polishing Soap (not intended for use on painted, clear coated or anodized surfaces) and/or Optimum Metal Polish and #0000 synthetic steel or bronze wool on the insides of the tips
Now move on to the outside of the tips once again with Optimum Metal Polish and an older microfiber towel that is no longer used for the painted surfaces, ensure to polish with the grain.
Note:
1. The inside of some vehicles exhaust tips are painted with a matte black heat resistant paint, do not use wire or bronze as this will remove the paint. This type of finish can be renewed by cleaning them well, and spraying High Temp Flat Black (Matte) Satin Paint that is available from n auto store (Dupli Color)
2. Dinan tips are titanium with the all-blue tip clean with soap and water. No use in using a metal polish as there's nothing to shine
Chrome Exhaust

[: chrome plating is a finishing treatment utilizing the electrolytic deposition of chromium. The most common form of chrome plating is the thin, decorative bright chrome, which is typically a 10-µm layer over an underlying nickel plate. When plating on iron or steel, an underlying plating of copper allows the nickel to adhere. The pores (tiny holes) in the nickel and chromium layers also promote corrosion resistance.

Bright chrome imparts a mirror-like finish to items such as metal furniture frames and automotive trim. Thicker deposits, up to 1000 µm, are called hard chrome and are used in industrial equipment to reduce friction and wear.][1]

Using chrome cleaner will remove the dulling that a car wash concentrate can’t. Apply a chrome cleaner (Semichrome or Mother’s Mag and Aluminium Polish) to a cool, dry exhaust, do not let the cleaner dry on the surface, for stubborn stains use #0000 synthetic steel wool and the metal polish.

To clean exhaust piping use a polishing powder (Blue Coral Blue Buster) to remove ‘blue’ from exhaust pipes wet towel and polish, it will not scratch chrome, can also be used on brass and stainless steel. Clean exhaust piping with Luster Strips. Protect the exhaust with a polymer (Zoopseal) sealant (See also Chrome / Stainless Steel Exhaust)

Recommended products-
a) Cleaning- any uncoated, non-ferrous metal surface – brass, gold, silver, aluminium, magnesium, pewter, chrome, sterling, copper, stainless steel – can be brought to a brilliant shine using Simichrome.
b) Protection - Zoopseal protects unfinished, brushed or polished steel, stainless steel, brass, aluminium and chrome parts from oxidation and eliminates the need for repeat polishing and extensive cleaning

Stainless Steel Exhaust Tips / Pipe

Stainless steel is a strong, robust and durable metal that far exceeds life spans of several other materials. Stainless steel is not just one material; it is a family of chromium containing steels, which all possesses an inherent resistance to corrosion. The chromium is distributed throughout the steel and its purpose is to form a sub-microscopic surface layer of hard, adherent chromium oxide on steel, a few microns thick.

The film is known as the passive layer, and it protects the underlying material from attack by corrosive species. If the layer is damaged in any way, it instantly reforms in the presence of oxygen to protect the surface of the material." To polish use a mild polish to remove stubborn stains use a polishing powder (Blue Coral Blue Buster or Blu-Job) to remove ‘blue’ from exhaust pipes wet towel and polish, it will not scratch chrome, can also be used on brass and stainless steel.

For exhaust pipe polishing -use a strip impregnated with a metal polish (Luster Strips) (See also Chrome / Stainless Steel Exhaust) protect the exhaust components with a polymer sealant (ZoopSeal)

Information resource-
• Caswell Plating website- http:// www.caswellplating.com/bbs/
Metal Polishing Secrets - http://www.topoftheline.com/metal-polishing-secrets.html
 
+1 on autosol, if it's bad get some 00 wire wool, don't worry, it won't scratch it, but will speed up the process alot!
 
Indeed the exhaust is covered with carbon deposits and etc. Where do i get this exotic stuff? I have some autoglym chrome cleaner and a micro fibre cloth at the moment lol
 
Another vote for autosol, I used it for the first time last week and was amazed how quick and easy it brought up my pipes. Far better than anything else I've ever used.
Exotic stuff??? Lol. Halfords or any motor factors sell it.
 
Used autosol, still cant get rid of the baked on carbon deposits, think im going to have to get out the wire wool
 
yep, if it won't get rid of it with a cloth, 00 grade wire wool is the only way mate, still may take some elbow grease, if that doesn't do it, I'm out f Ideas. Hope you get it sorted