Legal structure for your group
You have said that your organisation will not have members, will be charitable, will be led by volunteers and will be incorporated.
A possible legal structure for you is:
Charitable Incorporated Organisation (CIO) (Foundation model)
A Charitable Incorporated Organisation (CIO) is a type of charity that is incorporated. CIOs must be registered with and send annual reports to the Charity Commission. CIOs can either have voting members (Association Model CIOs) or be run by an appointed group of trustees (Foundation Model CIOs).
Your route so far:
Voting members? No. Charitable? Yes. Paid staff in charge? No. Incorporated? Yes.