It is understood a significant number of the special purpose soldiers, known as the Spetsnaz, have moved across the border and are spearheading the attacks.
The Russian army has overwhelming firepower and a large number of amphibious troop capability, Western officials have said.
They fear significant numbers of civilians will be killed if Russian ground troops go into Kiev and tens of thousands of people will flee the country in attempts to get away from the fighting.
They said large numbers of Ukrainians were seen fleeing to the west on Thursday morning after Vladimir Putin launched his attack sparking fears of a refugee crisis.
UK embassy staff have remained in the country to help Britons still in Ukraine.
The Prime Minister’s official spokesman said: “Our expectations are that the Ukrainian people will fight.”
He said that the UK were providing “defensive military capability”, including body armour to Ukrainian forces.
“In terms of refugees it is relatively early at the moment but we have already provided support at the border if we are to see a humanitarian crisis,” he added.