Investigators examining the beginnings of the 2016 probe of possible links between the Trump campaign and Russian election interference are pushing to complete their inquiry despite the coronavirus pandemic.

The former U.K. Ambassador to Russia, Sir Andrew Wood, who in 2016 alerted the late Republican Sen. John McCain about related allegations, said he had been contacted in connection with the probe. “My answer to an enquiry by email from a member of the team about 2016 some weeks ago was that I had nothing to add to what...