My letting agent placed my ex-tenant with new landlords knowing that she had caused damage to my house?

This is really marginal at best but it would be hard to prove they broke the law. I'd, of course, get a new letting agent, and you might want to also call the landlord of the new place and tell them the whole story - they have a right to know. You could also call her prior landlord and ask about this possibility but not sure what good this would do now, other than satisfying your curiosity.