Ukrainian forces have made "tactical progress" on the flanks of Bakhmut in recent days, according to UK Ministry of Defence (MOD) intelligence.
The beleaguered town in Donetsk Oblast has been at the centre of fierce fighting between Ukrainian and Russian forces for months, with the battle for Bakhmut the longest in the war so far.
The MOD said mercenaries of Russia's Wagner Group are continuing to make "gradual progress" in clearing Ukrainian positions in the town centre of Bakhmut.
However, according to the MOD's latest update on the situation in Ukraine, "over the last four days, Ukrainian forces have made tactical progress stabilising the flanks of Bakhmut to their advantage".
As well as progress to the south of town, the MOD intelligence says that "Ukrainian assaults have forced back the Russian frontline to the north-west of the town".
"This has likely enabled Ukrainian forces to re-establish more secure use of the key 0506 supply road, the update added.
"Ukraine is holding Russia's western advances along the line of Donets-Donbas Canal, turning the waterway into an obstacle as part of a deep defensive zone around the town of Chasiv Yar," it added.
The MOD reported over the weekend that Russian forces had fled Bakhmut "in bad order" as the Ukrainian military recaptured ground.
The MOD believed that Ukrainian forces regained at least 1km of territory in the besieged city.
"Over the last four days, elements of Russia's 72nd Separate Motor Rifle Brigade (72SMRB) likely withdrew in bad order from their positions on the southern flank of the Bakhmut operation," the intelligence on Saturday said.
"The area has some tactical significance because it was a Russian bridgehead on the western side of the Donets-Donbas Canal, which marks the frontline through parts of the sector.
"72 SMRB is an element of Russia's 3rd Army Corps, a formation created in Autumn 2022 and dogged with allegations of poor morale and limited combat effectiveness."
Kyiv hit by air attacks
Ukraine's capital city Kyiv has been subject to further Russian air attacks, with one official describing a strike as "exceptional in its density".
Serhiy Popko, head of Kyiv's city military administration, said in comments posted on the Telegram messaging app: "It was exceptional in its density – the maximum number of attack missiles in the shortest period of time,"
Ukraine has said that all 18 missiles fired by Russia were shot down.
Ukrainian Defense Minister Oleksii Reznikov said on Twitter: "Another unbelievable success for the Ukrainian Air Forces! Last night, our sky defenders shot down SIX Russian hypersonic Kinzhal missiles and 12 other missiles.
"Russian terrorists have no chance of prevailing over Ukraine. Their weapons can and should be countered by Western ones.
"Thank you to our Air Force service members and our partner states, who invested in securing the skies over Ukraine and all of Europe. Let's win together!"
Russia has recently launched a series of attacks, often targeting Kyiv, as Ukraine prepares to launch a counteroffensive to try to take back land occupied by Russia.