Can you get access to employment records held by the Royal Family?

My great grandmother worked for Lord Battenburg in London. She was a maid and after having children went back to work in the laundry. Apparently she would bring home second hand clothes from the job. Would there be a record of her being employed there. I don't know which residence it was. Her name was Mary Hurley nee Sullivan, originally from Ireland.

try cyndislist.com. There are loads of links there that might be helpful

I guess this was a long while ago, as the changed the name from Battenburg to Mountbatten in WWI as the former sounded too German. I also assume that your ancestor's employer was the father of Lord Louis Mountbatten. I can only suggest that you start looking either in the National Archives at Kew, or contact Broadlands, the home of Lord Louis:- http://www.broadlands.net/.
rdenig is right. The only place those records would be kept after all these years is in the National Archives. I doubt they're open to public scrutiny, but there may be something in there (such as diaries, journals or the such) that might helpful to you.