http://www.tssa.org.uk/article-46.php3?id_article=1382you can see loads more info here.
From an employers point of view, I really don't agree with it, but employees do have to be protected.
Of course any "new" business taking over a contract, will have to meet and agree new terms with their new staff. I believe you can't put rate of pay down. There is so much involved you may be just as well to contact ACAS.
Edward,
I'm not sure, but you may be able to get round it.... If your cleaner really wants to stay with you, they could resign and then you could re-employ them on different terms, as I said I am not sure you can do this, but then who would know.
Again all your cleaners has to do if he/she really wants to stay with you, is tell the new business, that they no longer require a job and give notice to them once the contract is transferred.
If the job has been tendered out, did you not get it because of price?