No, you don't need a Class 1, unless you want to be remunerated, in which case a CPL or BCPL is also required (hence Class 1).
I believe some BCPL holders who had the old UK class 2 and didn't qualify for a Class 1 have been granted a Class 1 restricted to the old BCPL limits.
An unremunerated PPL FI need only hold a Class 2