TUPE is one of those 'grey' areas that is open to a lot of interpretation.
In normal circumstances the cleaner would indeed have a solid case for transferring over to you. When I say in normal circumstances, I mean if they worked for a Contractor who had the cleaning contract and was employed specifically for that client.
As the Incumbent Contractor is (as you say) an agency I would challenge their right to transfer under TUPE legislation.
When someone starts work for an agency the conditions under which they are employed are normally such that they may be required to work at a number of different sites and for a number of different clients of the agency.
Only if the cleaner was employed by the agency SPECIFICALLY TO WORK ON THAT CONTRACT would they have any claim to transfer under TUPE. Ask to see the 'Statement of Terms and Conditions of Employment' which exists between the Agency and the Cleaner. If it doesn't state that they are employed solely for that position then they can forget it.
Furthermore, what is their length of service?
If it is less than 12 months they have no right to transfer anyway (even if they meet the criteria above) and if they did, they would have no claim at a tribunal if you then got rid of them through poor standards.
If they were employed specifically for that position and more than 12 months ago you may be forced to allow them to transfer but that is not the end of the world. They can be 'managed' out of the door.
Make it clear what is required of them and what will happen if they do not perform. They will soon leave when they find out they have to work for a living.
Read this
http://www.dti.gov.uk/er/tupe/consult.htmGood luck.