Hi Emsie
Its worth remembering that support through IAPT Wellbeing service, is for those suffering with mild to moderate symptoms. If they consider your symptoms to be more severe, they should refer you on to Secondary care and more intensive support with an experience psychologist.
Different counties across England all vary slightly, but you can be offered either, computerised guided CBT, telephone CBT, Group CBT or face to face 1-2-1 CBT. You have the right to ask for face to face 1-2-1 CBT if this is your preference.
I would make it very clear that you had already accessed CBT privately and the amount of sessions you had, as you may already have exhausted the level of support and knowledge offered through the Wellbeing team, and need more intensive support. They may need to step your care up to secondary care.
Take a look at the NICE Guidelines and the stepped care approach for OCD
https://www.nice.org.uk/guidance/CG31/chapter/1-Guidance#stepped-care-for-adults-young-people-and-children-with-ocd-or-bdd
Remember that your care should be stepped up if you do not achieve significant reduction in your symptoms at the end of your sessions.
Good luck, and well done for referring yourself.