I wasn't suggesting that the UK audit would actually audit the Cayman Islands company but it will clearly cover the funds being managed by them on behalf of ARK. They will want to know that the money is still there and producing a reasonable return.
ARK Schools which operates their academies in the UK is a charitable company, number 05112090. They are controlled by Absolute Return for Kids, a UK charity, company number 04589451. ARK Academies Projects is a wholly owned subsidiary of ARK Schools, set up to manage the building programmes needed for their first academies - company number 04101629. ARK UK Programmes, company number 05932797, is a wholly owned charitable subsidiary of ARK which provides extended school programmes at the academies.
ARK Schools does pay some money to ARK UK Programmes. Also to correct myself slightly, ARK pays rent, general office overheads and service charges on behalf of ARK Schools which then repays the relevant amount to ARK. The most recent accounts available show that they paid around £750k to ARK to cover these items and received over £3M in sponsorship funds from ARK.
For the sake of completeness, some directors of ARK are also directors of ARK Masters Advisers, company number 05443569, which provides investment advice to the Cayman Islands company (ARK Masters Management Limited). Some of the directors of ARK are also directors of ARK (South Africa), company number 4957091, which runs ARK's programmes in South Africa.
That appears to be the complete list of ARK Companies in the UK. I can't find any other ARK companies controlled by the trustees of either ARK or ARK Schools, although I haven't managed to get a full list of companies for Stanley Fink.