First, Sunak does not own any companies, and as far as I have been able to determine, he never has.
Hence Vixen's misguided invocation of the concept of company stewardship. There is the UK Stewardship Code, which covers some aspects of asset management, but this is not the same as a trust. The only overlap is that a fiduciary duty exists in both cases. And since the code is a more of a corporate governance standard, it includes many things that are not appropriate to trusteeships. It might apply to publicly held and traded companies, for example, where the corporate officers act by proxy for shareholders, but any private ownership interest such as that attributed to Sunak is not relevant.
Second, Sunak has investments that are controlled by what the the Independent Adviser on Ministers' Interests characterized as a "blind management arrangement," as I mentioned earlier.
Vixen seems to be laboring under the misconception that a trust is not legally enforceable or morally justified unless it has somehow been registered for public inspection and that its parties must be disclosed publicly. No such obligation exists, and Vixen's unwillingness to recognize the validity of a blind trust seems to be based entirely on rules she has made up. The identity of the trustee need not be disclosed. The terms of the trusteeship need not be disclosed. It is a simple contract. It is valid and legally enforceable insofar as it has been properly executed by the parties to it.
A trust is the object of a trusteeship, which is created by a private contract between the trustee and the beneficiary for the management of some property or interest. Necessarily the trustee has limited power of attorney to exercise the interest in a market. The contract usually requires the trustee also to be a fiduciary, meaning there is a legal obligation for the trustee to act in the beneficiary's best interest when so acting. A blind trust adds the provision that prevents the trustee from disclosing the structure of the interest under management in a way that the beneficiary could reasonably discover. The identity of the trustee need not be disclosed publicly, however the trustee will necessarily need to prove his power of attorney when doing business on the beneficiary's behalf. That disclosure need not be public, and may certainly be guarded by non-disclosure agreements—especially to implement the provision against allowing the beneficiary to become aware of transactions involving the property in trust.
Obviously controversies that may arise in the operation of the trusteeship may come to court, in which case the parties will necessarily be disclosed, and possibly also the structure of the interest in trust. However, the legal posture of litigation is usually agreed to by the parties and may provide, for example, for binding private arbitration.