They also warned that the “shortcomings” of Mr Putin’s military planners and a “shortage” of Russian precision missiles was likely to lead to more atrocities with civilians being killed.
In its latest intelligence update, the Ministry of Defence in London said: “There is a realistic possibility the missile strike on the Kremenchuk shopping centre on 27 June 2022 was intended to hit a nearby infrastructure target.
“Russia’s inaccuracy in conducting long range strikes has previously resulted in mass civilian casualty incidents, including at Kramatorsk railway station on 9 April 2022.”
It added: “Russian planners highly likely remain willing to accept a high level of collateral damage when they perceive military necessity in striking a target.
“It is almost certain that Russia will continue to conduct strikes in an effort to interdict the resupplying of Ukrainian frontline forces. Russia’s shortage of more modern precision strike weapons and the professional shortcomings of their targeting planners will highly likely result in further civilian casualties.”
Mr Putin’s army was also reported to make more progress in the eastern Donbas region where he is focusing his military campaign.
The MoD added: “Russian forces continue to make incremental advances in their efforts to encircle the town of Lysychansk. Since 25 June 2022, Russian forces have advanced a further 2km near the Lysychansk oil refinery, south of the town.”
The search was continuing on Wednesday for dozens of people still missing after the missile attack on Monday on the shopping mall in Kremenchuk in central Ukraine.
At least 20 people were reported to have been killed and more than 60 needed treatment for injuries.
Ukraine said Russia had killed civilians deliberately when it pounded the retail complex.
"Russian missile hit this location precisely. Deliberately ... It is clear that Russian killers received those exact coordinates," Ukraine's President Volodymyr Zelensky said in an evening video address. "They wanted to kill as many people."
Authorities said around 36 people were still missing in Kremenchuk.
Moscow said its military was seeking to strike a nearby arms depot.
In the south of the country, eight missiles struck the city of Mykolaiv including an apartment building, Mayor Oleksandr Senkevych said.
Photographs from Mykolaiv showed smoke billowing from a four-storey building with its upper floor partly destroyed.
Further east in Lysychansk in the Luhansk region, a key battleground in Russia's assault on the industrial heartland of Donbas, the governor reported increased military action.
The situation in Lysychansk resembles that in its twin city Severodonetsk more than a month ago when the Russians started taking building after building, Serhiy Gaidai said on Wednesday. Severodonetsk fell to Russia on Saturday.
"The Russians are using every weapon available to them ... and without distinguishing whether targets are military or not - schools, kindergartens, cultural institutions," he said on television.
"Everything is being destroyed. This is a scorched-earth policy."
Russian forces are trying to surround Lysychansk, Ukraine's armed forces general staff said on Wednesday.
Russia has denied targeting civilian areas during its four-month offensive against Ukraine, a claim which flies so blatantly in the face of numerous reports, footage and photos from the war zone.
The United Nations says at least 4,700 civilians have been killed since Mr Putin launched his invasion on February 24, with the real figure widely believed to be significantly higher.
In the Dnipropetrovsk region, towards Ukraine's east, Governor Valentyn Reznychenko said bodies of a man and a woman had been found buried under the rubble of a transportation company office that was hit by a Russian missile on Tuesday.
Separately, Russia-installed officials said their security forces had detained Kherson city mayor Ihor Kolykhayev on Tuesday after he refused to follow Moscow's orders. A local official said the mayor was abducted.
The Moscow-imposed military-civilian administration in Kherson region said it had begun preparations for a referendum on joining Russia, Russian state news agency TASS reported.
Kherson, a port city on the Black Sea, sits just northwest of the Russian-annexed Crimean peninsula.
In the past few days, Ukrainians have also described attacks in the southern region of Odesa and Kharkiv in the northeast.
Valery Zaluzhny, chief commander of Ukraine's armed forces, said on Telegram app on Tuesday that Russia had fired around 130 missiles on Ukraine within the last four days.
The Russian invasion, the biggest assault on a European state since World War Two, has driven up prices of food and energy worldwide and fuelled global security worries.
Finland and Sweden on Tuesday moved a step closer to joining the Western NATO military alliance in response to Russia's actions, after Turkey dropped its opposition to their membership.