A collective investment scheme is a trust, and a trust needs a trustee. The corporate trustee holds the scheme's assets in trust for the unit holders and is legally obliged to act in their interest — including against the fund manager where the two conflict.
Its job is to check that the manager is following the scheme's own rules: what it may buy, how much of any one thing it may hold, how units are priced.
Appointed by the scheme, not chosen by you. The trustee's name is in the fund's information memorandum, and a fund that cannot readily tell you who its trustee is has answered a different, more important question.
None. It is a cost to the scheme and a protection for you, and it is already inside the rate a fund quotes rather than taken off afterwards.
The presence of a trustee is one of the clearest tests of whether something is a real fund. An unlicensed scheme has nobody independent holding the assets, which is precisely what makes the money disappear when it disappears.
The full list is on the regulator's own page, which is where it stays current.
See the live list at the CMA
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