Most people on here will be in a position to tell you this but it's unlikely that you can enjoy the best of both worlds - a restraint of trade clause in an employment contract is fairly simple and, so long as it's temporally and geographically reasonable, could possibly be enforced against an ex employee who has exploited the information gained in paid employment for financial gain. When a sub contractor tries to get between you and your customer, you'd possibly have a tortious interference or inducement to breach claim but it would be an ill advised course of action between you and anyone who you take on to carry out personal services and would cause more problems than it could ever solve.
In an employment contract, you'd have something which runs along the lines of
"I agree not to take on any works within 3 miles for a period of six months following last instruction for xxx ltd and that a £500.00 payment will become due on each breach of this condition"
that would possibly be sufficient deterrent for potential cleaning entrepeneurs to be dissuaded, though I have to say it wouldn't stop me..