Yes you can rent a private house in an IVA as long as the rent is not too exorbitent.
Sharing from experiences of dealing with debt
The greatness of a man is not in how much wealth he acquires, but in his integrity and his ability to affect those around him positively.
Bob Marley. http://kallis3.blogs.iva.co.uk
Are you renting already? and yet to start an IVA?
The rent will be part of your monthly outgoings so as long as already mentioned its not above the local norm(price wise) it should be ok.