There are probably many trusts managed by companies (private trust companies?) especially formed for that purpose.
The use of private trust companies offshore is increasingly popular and is seen as enhancing the confidentiality of the trust.
There is probably no fundamental reason why such companies cannot act as trustees of a trust within the UK.
Whoever has the power of appointment of trustees will be exercising a fiduciary power and will need to be satisfied as to the competence of the newly formed companies (or, probably more correctly, their directors) to act as trustee.
Issues that could be of concern include:
As they each have a nominal share capital, they are the corporate equivalent of men of straw and may be unable to satisfy any claim against them that might arise in the future
If those responsible for running the companies are also beneficiaries, the exercise of any trustee powers in their favour could be impeachable
As they are not trust corporations, neither can be a sole trustee nor enjoy any other benefit that applies to a trust corporation
As a corporate trustee, they may need to register with HMRC to undertake trustee business
I suggest it is a case of understanding the rationale why companies should be trustees in the present instance, rather than individuals, which will ease concerns over the proposed arrangement.