I can buy a servicemaster franchise in anyone of about 20 areas and in a month clean with your equipment. Hardly skilled .
Carpet cleaning is not a skilled job , it is low skill, electricians , plumbers, joiners , they are skilled trades .
Lets take your days work , it is worth £150 at best , plus £150 to hire van and equipment , plus materials and fuel £100 , plus profit , that is where you get the £500 from .
Your customer is quite correct in saying you are just a cleaner , what she needs educating in is the fact that she is hiring a lot of expensive kit too , not a couple of grands worth of tools that a tradesman will have.