Drugmakers, including BioNTech and Moderna, are scrambling to test their Covid-19 vaccines against a new fast-spreading variant that is raging in Britain, the latest challenge in the breakneck race to curb the pandemic.

Ugur Sahin, chief executive of Germany's BioNTech, which partnered Pfizer to take less than a year to get a vaccine approved, said on Tuesday he needs another two weeks to know if his shot can stop the mutant variant of the virus.

Moderna expects immunity from its vaccine to...