In Halliburton1, the Court of Appeal of England and Wales has held that the arbitrator had a duty to disclose that he had other appointments in proceedings which could be of interest to one of the parties, but that the lack of such disclosure was not creating doubts as to his impartiality
1 Halliburton Company v. Chubb Bermuda Insurance Ltd., Court of Appeal of England and wales [2018] Civ. 817.

