The letter adds to tension between the European Union and the U.S. drug-maker, which announced last week a temporary slowdown in deliveries to the bloc.
On Saturday, the UAE recorded 3,566 Covid-19, a new high for the 12th consecutive day. It has so far recorded over 274,000 infections, including 783 deaths.
Johnson said that the impact of the new variant, which is already known to be more transmissable, was putting the health service under “intense pressure”.
The move came a day after Reuters reported that Amazon had offered to help with the United States' efforts involving the COVID-19 vaccine, citing a letter addressed to President Joe Biden.