It is likely that the shares are held by a family trust or an offshore company registered in another jurisdiction, rather than being held personally by him. Although I am not familiar with the UK's tax laws, in other countries, loopholes exist that allow for taxable income from dividends of shares held personally to be reduced or eliminated through capital loss and depreciation deductions.
I don't know anything about his tax arrangements but he lives in South Kensington (in London) I think. I seem to recall reading about one of those classic South Ken arguments with neighbours because of him building a basement swimming pool or something.
He's our Prime Minister's old boss as well. Rishi Sunak used to work for TCI[1].