He said the 100 migrants on his boat cheered as they saw Royal Marines from HMS Bulwark come to rescue them on Sunday morning.
Mr Cessay said he left Libya because it was dangerous, and told how he gave all his money to Arab people-smugglers who assured him he could get into any European country.
He added: 'Libya was very difficult. They took my money, they made me work but did not pay me and if you talked they said they would kill you.
'They told us in 15 hours you will be picked up. I knew I could die but I didn't care. When we saw the British we cheered. Some women cried.'
Mrs Balla said: 'I want to go to Europe to save my children's lives.
'My husband took the boat two months ago and we are going to join him in France.'
Cradling her two-year-old daughter yesterday and keeping close to her three boys aged 11, eight and six on HMS Bulwark, she said she was forced to leave Sudan three years ago because of the war there.
Henry, who travelled from Nigeria to Libya to make the journey, said: 'I want to go to England. But anywhere they take me in Europe I know that will be fine because Europeans care for human beings.'
The 1,100 migrants arrived in Italy on the 19,000-tonne Royal Navy assault ship after travelling for ten hours overnight from Libya.
On arrival in Catania, Sicily, each was photographed and given a number by Italian authorities.
They will be bussed to refugee camps all over Italy where they can claim asylum. But many of them have no passport or papers, and can easily slip into northern Europe.
One Navy source said: 'They give us a name, but we have no idea whether it is the right one.'
Am Jordan left Ghana in December and crossed the Sahara to Libya for a better life.
The 19-year-old said: 'I left behind my dad, my sister, my brother. It was not easy.'
He had not intended to go to Europe because he thought Libya would be safe.
But he added: 'When I got there I saw it was even worse than Ghana, so I decided to move on.' All he took was water and a bottle of Pepsi. 'I don't have a passport or any papers. I have come empty handed', he said.
Dawud Sherif, 17, also from Ghana, said of the journey: 'I knew I could die but I was ready to because I felt dead already. I am just happy I am alive. I wanted Europe to save my life.
'Life in Ghana was not worth living.'
Pregnant Nigerian Favor Richard, 29, went into labour on a rubber craft packed with refugees as Royal Marines arrived.
She was taken by helicopter to hospital in Malta, where she gave birth to a boy on Sunday night.
- Daily Mail