I have worked from both as a self employed therapist. Each council is different but if you're a good tenant and running your business won't cause a problem with the neighbours, (parking, noise etc...) they generally don't have a problem but you must tell them. Depending on the services you will offer you may need a Special Treatment Licence from the council, in my experience they have been very helpful.
Renting privately the above applies but you must obtain the permission of the letting agents & owner of the property. Maybe I was lucky but I was given permission and it worked really well for me. Just ask the landlord/agent and see what they say and take it from there.
Good luck x