They stressed that he was unleashing “large numbers” of missiles which are normally used to target sites of “strategic importance” but are instead being used to gain “tactical advantage”.
They argued that the combat effectiveness of his military units was becoming so degraded that it is “probably unsustainable in the long term”.
Mr Putin’s troops seized control of the eastern industrial city of Severodonetsk over the weekend.
They are now trying to capture its twin city of Lysychansk, across the Siverskyi Donets river from Severodonetsk in the eastern Luhansk province of the Donbas region.
In its latest intelligence update, the Ministry of Defence in London said: “Ukrainian forces continue to consolidate their positions on higher ground in the city of Lysychansk, after falling back from Severodonetsk. Ukrainian forces continue to disrupt Russian command and control with successful strikes deep behind Russian lines.”
It added: “Over 24-26 June, Russia launched unusually intense waves of strikes across Ukraine using long-range missiles. These weapons highly likely included the Soviet-era AS-4 KITCHEN and more modern AS-23a KODIAK missiles, fired from both Belarusian and Russian airspace.
“These weapons were designed to take on targets of strategic importance, but Russia continues to expend them in large numbers for tactical advantage.”
The British defence chiefs also stressed: “Similarly, it fielded the core elements of six different armies yet achieved only tactical success at Sieverodonetsk. The Russian armed forces are increasingly hollowed out.
“They currently accept a level of degraded combat effectiveness, which is probably unsustainable in the long term.”
Britain, America and other allies are fighting an information war against the Kremlin, so its intelligence reports need to be treated with caution, and often highlight Russian failures or shortcomings rather than Ukrainian losses.
However, the Russian propaganda machine often appears at complete odds with the truth, including the suggestion that a missile strike which hit a crowded supermarket in Kremenchuk in central Ukraine was an act of provocation by Ukrainian president Volodymyr Zelensky’s forces.
More than 1,000 people were inside when two Russian missiles slammed into the shopping mall in Kremenchuk, Poltava, Mr Zelensky said.
Britain has condemned the attack as an “act of terrorism” by Mr Putin’s military.
Emergency crews were still searching for survivors in the rubble of the shopping centre.
At least 18 people were killed and 25 hospitalised, while about 36 were missing, according to civic chiefs.
Meanwhile, Russian troops and their Luhansk Republic allies were advancing into Lysychansk and street battles had erupted, said the ambassador to Moscow of the Luhansk People's Republic, recognised only by Russia.
Ukrainian forces still controlled Lysychansk but its loss was possible as Russia poured resources into the fight, Luhansk provincial Governor Serhiy Gaidai said.
The Russian army has also again shelled the eastern city of Kharkiv, reportedly hitting apartment buildings and a primary school, killing five people and wounding 22 including children.