Asking this mostly so I can answer it in case it helps others. I had been provided a csv that was doing as described in title ie it had both custom and core fields in it, and the core date eg First, Last, Email etc were importing but the Custom fields were not being imported.
I took a stab in the dark on this and re-ordered the columns in the csv to ensure that the custom fields did not come before the core fields. This resulted in both core and custom data to be imported. This may be documented somewhere but was a new one for me.