Aga range cooker side panels are unique, there is no other part of your cooker that is the same. It's not enamel or stainless steel but in fact is simply painted tin. They match the front colour of your cooker of course but unlike enamel it's not very tough, in fact it is very easy to damage!
Luckily it can be cleaned when the cooker is on, the secret is soaking. You can scratch the paint finish very easily using wire wool or strong scouring pads so to start with pop some towels down and soften the grease and muck using lots and LOTS of hot soapy water, Fairy liquid really is an extraordinary degreaser!
Agitate the suds gently with a soft (ie very old) scouring pad or even just a normal sponge. It's best to do this while doing other things so you don't get impatient! How long it will take will very massively but you need to soften the grease that is dried on - keep your soapy water HOT! If necessary I'll do this over several hours while I am on-site at most jobs.
Over time this method should dissolve most grease marks but sometimes you just have to get a bit tough with the scouring pad (never wire wool) and give a good scrub. Done gently you can avoid most damage to the paint finish but some 'lightening' is likely.
If your side panel is really damaged then replacing it is a real pain as all the insulation inside immediately falls out when you remove the panel. Consider re-painting the panel instead (radiator paint is a good option) or hiding it altogether with a strategically place shelving unit created by a friendly carpenter or joiner!
Hope that helps, get in touch if you have any questions!