Mr Kumarasiri, who runs Sneinton Boulevard Post Office, says all immigrants in Britain should learn the language.
The 40-year-old, who moved here 18 years ago, says it is important to embrace British culture.
"If you come to Britain you have got to speak English," said the father-of-two, who is also a Liberal Democrat councillor on Gedling Borough Council.
"I am from a different country but when I came here I became British. My job is to give a service. I cannot give a service if they cannot tell me what they want."
Mr Kumarasiri, who helped raise thousands of pounds after the tsunami hit his native Sri Lanka, said he had banned about half-a-dozen customers.
"Some of them say 'you are not British'," he said. "I keep telling them 'don't come here or I am not going to help you'.
"One of the Asian ladies said 'you have a different language, why can you not speak that?'
"I said 'When I am in Britain I speak English.' Ethnic minorities came to this country to change their lives. They have to take pride in the country where they live. It shows that they care."
Banned customers who have returned with interpreters have been served.
Mr Kumarasiri, of Carlton, is campaigning for people of all races to feel proud about being British and has started a website – www.britishnessforever.co.uk
He said: "This is about unity among the people in this country who are proud to live here, whether they are Asian, black or white.
"Ninety-five per cent of people are proud to be British but they are scared to show it.
"It is being put into people's heads that you cannot say things to upset the minorities.
"The white person cannot stand up and say anything because they automatically become a racist."
He said people in Sri Lanka were proud to be associated with Britain, stemming from its days as a colony.
"Still we have the pride that Britain left behind," he said. "The laws are still there, the schools are still there. The kids have courtesy. They have discipline. Here all that is gone. Let's bring back all this."
Afzal Sadiq, chief executive of the Nottingham and Notts Racial Equality Council, said: "You are denying somebody a service that is there for everybody. It is not just there for everybody who can speak the language. (He also called Mr Kumarasiri a racists on a tv interview)
"In an ideal world these people would speak English. In the long term I understand the aspiration, but learning to speak English is going to take time.
"I would hate for them to be refused a service from the post office that is meant to be there for everybody. To deny someone a service is wrong.
"What about those people who cannot speak? What about those people from the deaf and dumb community?
"These are equality issues for me."
