Since no one has answered in more than a year, I will provide an incomplete (and possibly incorrect) answer:
CREST charges an "international custody charge". The amount charged varies by the country of the underlying security. As of August 2020, the fees range from 1.50 basis points (i.e. 0.015% of the value of the security) per year for US securities to 5.50 basis points (i.e. 0.055%) per year for Portuguese securities.
I found the above information through the CREST system tariff webpage where I found the tariff brochure: Euroclear UK & Ireland tariff - August 2020 (see section 6.2. International custody charges). These links are not indexed by search engines, and are only accessible by going through the MyEuroclear login webpage, and clicking on "Access as a guest / public information". (Why does it have to be so incredibly difficult to access information relevant to retail investors?)
Screenshot of the relevant tariff table (August 2020):
Much of the information I provided above is corroborated by this document: Questions and Answers for Holders of Barrick CDIs that happens to explain CDIs to UK shareholders who received shares in Barrick due to its merger with Randgold in 2019.
This answer is incomplete because it is missing the following information:
- How the fees are charged in practice (deducted from dividends? subtracted from brokerage account balances?).
- How often the fees are charged in practice (monthly? quarterly? yearly?).
- How the exact amount of fees is determined (is the percentage fee based on the closing price of the security on a specific date?).
- Whether or not there are other fees besides the "custody charge".