Marly,
You and I work the same areas so I can give you an insiders view of pricing in that area.
1.) Virtually all of the high price work is done on recommendation. When you are recommended you can charge those prices and more - no problem.
2. ) The high price work tends to go to carpet and upholstery specialists as opposed to general cleaning companies. If you buy a multi million pound home and fill it with expensive furnishings you look for a specialist with a long established reputation. Number 1 worries are security and will they ruin my £15,000 sofa - price comes much further down the list.
3. ) The lower price work tends to be rentals, small domestic, hotels, small businesses etc. They would rarely get 45 per sq ft as this market is more price sensitive and competitive. Much of this work is done by general cleaning companies and price is very important in getting the work.
Sounds to me like you need to do a few site surveys to get a feel for your carpet cleaning market and be more flexible in your pricing policy. There is a world of difference in cleaning carpets in Kensington Palace Gardens vs North End Road. Technically they are both in Central London but price wise they are worlds apart.
Nigel