Both sides were launching raids in small boats to seize the islands and attack the opposite riverbanks held by their enemy, they added.
In its latest intelligence update, the Ministry of Defence in London said: “Through the first half of September 2023, heavy fighting has continued around the islands in the lower Dnipro in Kherson Oblast (province), which currently marks the front line.
“Both sides have launched raids with teams in small boats against the islands and against the opposite riverbanks.”
The briefing added: “There is a realistic possibility that Russian operations in the area have been energised since the sector came under the responsibility of the newly created 40th Army Corps.
“The number of forces involved are relatively small compared to other fronts; however, both sides see the area as strategically important. It also provides the opportunity to draw their adversary’s units away from the intense combat in Zaporizhzhia and Donetsk oblasts (provinces).”
The update came less than 24 hours after the commander of Ukrainian ground forces said that they had “breached” Russian defences near the eastern town of Bakhmut which has seen the heaviest fighting of Vladimir Putin’s war.
General Oleksandr Syrskyi hailed the recapture of the eastern villages of Andriivka and Klishchiivka near Bakhmut.
Russian attacks across Ukraine were continuing with the western city of Lviv rocked by blasts in the early hours on Tuesday, with local officials saying the Russian air strike injured one man and caused a major fire at an industrial warehouse.
"A woman and a man were found under the rubble in Lviv. According to preliminary information, the woman was not injured. The man is in a serious condition," Lviv's region Governor Maxim Kozitsky said on the Telegram messaging app.
The scale of the attack and full extent of the damage was not immediately known. There was no immediate comment from Russia.
Lviv city mayor Andriy Sadovyi said air raid alerts for the region were called off after nearly three hours in the early morning.
Ukraine’s air force said 27 out of 30 Russian drones launched overnight had been shot down.