Abi, a sub-contractor will be a carpet cleaner the same as you, so they will have there own business, van, equipment, etc.
you simply send them to job, they invoice you, say £150 you invoice the client say £200. your cut £50.
i agree with John thats by far the easiest route, if upping prices is not best idea.
trouble with employing someone is youll need at least two big jobs a week just to pay them plus tax, then you need profit from there input too, as why else employ them. problaly be better get them a van send them out but you have to have stacks of work coming in for that. oh probaly worth taking note of Shauns findings on that subject, on money matters topic.