Thanks for this Lee Josepho.
I am not so sure of the assumption of the adding /new/ on the end of the original site name - I just tried this and it does not work. Additionally in looking at databases stored under sitename.com and new.sitename.com they are completely different - here I am looking at the list of databases not just the ones being used.
While I had asked the hosting company for a sub-directory to assemble this new site, in practical terms the new.sitename.com appears to be acting as a completely new domain name and that is how it appears in the CPanel.
It seems to me that in taking the path that I propose I may be doing a bit of overkill potentially, but it should work fine. Is that a reasonable take on this?
Thank you so much for your help and for your patience with this newbie.
I will be speaking to the 365 team tomorrow to try and iron this out.
Once again many thanks, your comments are really appreciated.
John