We are driving east along the south coast of Ukraine towards the port city of Mykolaiv.

Coming towards us on the other side of the road is a convoy of buses and they are hurtling along, about 15 of them, each one carrying scores of frightened residents who have fled this terrorised city.

This is how the people of Mykolaiv escape – because this is the only safe route out.

We are heading into the city, past checkpoints and barricades, until we reach a bridge which stretches over the Inhul river that runs through the city.

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If the Russians damage this bridge, no one will be able to escape without venturing into Russian military-controlled territory.

Mykolaiv has been under sustained attack for more than a week now. The streets are deserted. There are piles of old tyres on nearly every street corner, primed with molotov cocktails. Defence forces intend to set them on fire in the hope the thick black smoke will slow their enemy.

Ukrainian officials accused Russia of damaging a cancer hospital and several residential buildings in the southern part of the city following a bombardment of shelling from heavy artillery.

The night before we arrive, 53 people were injured – including seven children – after a series of attacks.

Half the city’s population has fled: 250,000 people in just under two weeks. And those who cannot leave are forced to hope for the best.

Larysa is a 68-year-old grandmother who we find queueing with her two grandchildren, aged one and six, outside a shop near to the city’s main hospital. She tells me she can’t leave.

“I had a different opinion of Russia but after all the explosions and bombing, when all the windows are shaking and when I’m holding my grandchildren in my hands, I have changed my mind. The only thing I want to say is: This is my homeland.”

But this is no place for children. Not now. Not with the shells and the bombs.

The governor of Mykolaiv, Vitaliy Kim, has become something of a social media hero, posting videos several times a day.

He even donated his convertible sports car to the local police who promptly welded a machine gun to the back.

At a news conference, Kim said the Russian advance had been slowed and suggested those still in the city should stay at home.

I ask him if Russia is targeting civilians.

“I am sure they are targeting civilians because it corresponds with their goals – they target electricity, gas, heat. This is what they do.”

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Asked if he has the resources to fight, he replied: “By all means, our main resource is our will.”

On a street corner, some people queue for a clinic which is dispensing medicines to the vulnerable.

We meet eight-year-old Misha and his father Alexey, himself a former soldier who says he suffered from post-traumatic stress. He is picking up the tablets he needs to help his condition. He tells me he does not want his son to witness war like he did.

“Misha understands what is happening. He understands who the aggressor is. Yesterday he cried. It hurt me when he said ‘what does Putin wants from us? When will this war end?'”

I ask Misha what he thinks of what is going on around him.

He says: “My parents wake me up and tell me about the bombing. And the first thing we do is hide in the shelter. To save ourselves.”

They begin the walk home. It is Misha’s birthday in the morning – he will be nine. He says he is hoping for a good day.