There are several insects that this could be, moths being just one of them. There are others - amongst the most common are carpet and fir beetle. Of the 5,000 plus pest species that exist in the u.k. carpet moths do no exist but there are species that will lay their eggs in wool carpet.
The adult insects lay their eggs in a food source for the larvae, the wool carpet, so once the larvae emerge they crawl through, eating away, before spinning a cocoon to emerge as adults and take off. Damage is in corners of room around edges and under furniture. When the damage is noticed it is normally after the larvae have developed so treating with some thing like permethrin which only has an active period of 30 days is just ripping your customers off as it will not serve any purpose. There are products that remain active for a much longer period (up to 12 months but these products are controlled and regulated.
These pests will often return to the same site in the next season and it is then that the insecticide needs to be active to break the chain.
Even with permethrin, a product that is widely available, once you start charging for this type of work you need to comply with the legislation that covers how these products are used, applied, stored and who you expose to them.
It may be a complete surprise but these products are dangerous things and need to be treated with respect. You need to also control your own exposure to these product as they are harmful to you. Pest control is not a closed shop and anyone can join but training is needed and a carpet cleaning website is not the place to be discussing this. Training is available from
www.bpca.org.uk/ or the best is probably
http://www.rsph.org.uk/. I have read a lot of naive, irresponsible and very stupid things said on previous posts regarding fleas and the like and cringe when I read them. If you would like to be educated in pest control then go to the people who are qualified to teach you. You are discussing using hazardous chemicals in front of people who do not even understand the fundamentals of their own industry. I have no teaching qualifications myself so do not take it upon myself to instruct you.