People who are seeking to come to the UK to work or to join a spouse already living here should be required to learn English, the Commission on Integration and Cohesion says.
It wants ministers to consider changing immigration rules to ensure new arrivals have some command of the language before being allowed to come as a worker or through marriage.
But under current proposals, only migrants who are unemployed or on benefits will qualify for free English lessons from September.
Here, three people who came to Britain with little or no English language skills describe the challenges they would face learning English in their home countries and how lessons at London's Lewisham College have changed their lives.
Ikram Ahmed, 26, from Somalia
"I have been in Britain three years, but I started learning English last year.
"I didn't speak any English before I arrived because I didn't go to school. I couldn't read or write.
"I left my family in Somalia because of the situation there and came here with my daughter who is eight years old.
"She goes to school here and she is better than me at English. She sometimes corrects me.
"When I came it was very difficult. I couldn't understand anything. When someone asked me a question, I couldn't answer.
"Now, I am gaining confidence to speak.
"I would not be able to study English in Somalia because there are no schools there now. Before, when there were schools, I would have to pay.
"I think it is important for people to learn English. It took me two years to be able to communicate, and I have a lot of friends here at college.
"I enjoy learning and it is important to get a job, to communicate with people and to understand.
"I don't work now, but I would like get better at English and to work in nursing."
Adrian Zajac, 25, from Slovakia
"I came to Britain two-and-a-half years ago because I wanted to learn English. I came because I think England is the best place to learn English.
"I didn't study English in Slovakia because the schools are not so good.
"If we want to learn properly, we have to be very rich - we can pay an English teacher.
"Most people can't afford it.
"When I came here I didn't know any English at all.
"When I came to college for the first time, I couldn't understand when the course started. So, I ended up starting six months later.
"Everything was difficult, but life is much easier now and I am able to join in British life more.
"I would like to carry on studying and go to university. I quite like England - there are more opportunities for me here."
Ahoua Diomande, 30, from Ivory Coast
"I came to Britain five years ago because there was a war in my country. I left my family behind, but two years later my brother came to join me.
"I learnt English at college, but you have to pay for it. It is very difficult for most people to do that before coming.
"For most people when they have the chance to come to Britain, they haven't studied English and it is very difficult for them to speak. I think they need help.
"Learning English is very important for me. When I first came to England, I could only speak French. From that moment I didn't know what to do or where to go.
"Once, I was standing on a bus and I was lost. The driver could see I was lost, but he couldn't understand my French. It was very difficult.
"I started learning English three years ago, and now I am always at college.
"I work in a hospital as a cleaner - but I hope to improve my English more.
"People coming to Britain find it difficult to learn English because it is not their first language.
"When they are at home it is difficult to learn, they will not learn until they come to Britain.
"Now I communicate with English people - they speak slowly so that I can understand. I can understand all they are saying."