He said that using British-supplied equipment to do so would not be a problem, despite past caution among allies keen not to antagonise President Vladimir Putin.
Downing Street said Mr Heappey was speaking on behalf of the Government but argued deciding on the location of strikes was a matter for Ukraine.
Defence sources said he was referring to an attempt to stop the bombardment of Russian artillery, rather than striking targets in Russian territory.
“The UK and many other Western allies are now providing longer range weapon systems to help counter the indiscriminate artillery fire that the Russian Armed Forces have been raining down on besieged Ukrainian cities,” a UK defence source said.
“Targeting is a matter for Ukraine, but the UK expects all parties in this conflict to decide on their military targets in full compliance with the laws of armed conflict.”
The Downing Street spokesman added: “I think what is clear is that we are providing Ukraine with the capabilities to defend themselves.
“Ukraine was living peacefully within its borders and then Russia invaded as the Minister made clear that Ukraine needs to strike Russian logistics fuel supplies, ammunition depots and it is not for the UK to dictate how they go about defending themselves.”
Mr Heappey told Times Radio it is “completely legitimate for Ukraine to be targeting in Russia’s depth in order to disrupt the logistics that if they weren’t disrupted would directly contribute to death and carnage on Ukrainian soil”.
He said it was “not necessarily a problem” if British-donated weapons are used on Russian soil, given the weapons supplied to Ukraine have the range to be used over borders.
But he dismissed Russian Foreign Minister Sergei Lavrov’s claims that Western allies are “pouring oil on the fire”.
Mr Lavrov has warned that the threat of nuclear conflict “should not be under-estimated” and warned Nato against provoking “World War Three”.
But Mr Heappey told BBC Radio 4’s Today programme that the chances of nuclear warfare are “vanishingly small”.
“All of this noise from Moscow about somehow their attack on Ukraine being a response to Nato aggression is just utter, utter nonsense,” he said.
Britain is sending a small number of Stormer armoured vehicles fitted with launchers for anti-aircraft missiles in the latest shipment to repel the Russians.
Defence Secretary Ben Wallace said on Monday Ukraine needed more long-range artillery and ammunition, as well as anti-ship missiles, and said the UK was seeking to supply such weapons.