"The last few days have shown that we can move forward and destroy the enemy even in such extremely difficult conditions," he said.
The Kremlin, for its part, said it did not believe the added British hardware would change the course of the conflict.
Moscow has acknowledged retreating north of the city, and the head of the Wagner private army fighting inside Bakhmut has said Russia's regular forces have fled positions on the northern and southern flanks.
The public rift between Wagner founder Yevgeny Prigozhin and the commanders of regular Russian forces has deepened over the past two weeks, with Prigozhin releasing daily audio and video messages denouncing the Russian military brass.
However, both he and the Kremlin dismissed a Washington Post report citing U.S. intelligence leaks that Prigozhin had offered to betray the positions of regular Russian forces in January in return for Kyiv pulling back some troops in Bakhmut.