In May the Prime Minister, David Cameron announced plans to give police the power to limit what he described as the "harmful activities" of an extremist - under new anti-terror legislation.
"Eighty per cent of people surveyed agreed that policies designed to counter extremism may make it harder for Christians to express their faith in public," said Dr Dave Landrum, director of advocacy, EA.
"There are concerns about the government's overreacting to fears about radicalisation and terrorism in a way that might undermine the very freedoms that the government is purporting to protect.
"A similar number believe that freedom of speech needs greater protection in the UK than is presently provided," added Dr Landrum.
According to evangelicals, the Christian faith has played a key role in providing values to British society throughout its history, but this legacy is swiftly eroding.
The survey showed that the vast majority of respondents (93 per cent) agreed Christianity had strongly shaped historic British values, but less than a third (31 per cent) felt it still shaped values today. Fewer than one in five (18 per cent) agreed that Britain is a Christian country.
The Home Secretary, Theresa May, has said that the government's strategy would include new legislation likely to include powers to take action against individuals or groups who are considered to be espousing extremist views, but denied it would constitute an attack on freedom of speech.
1,700 evangelicals were questioned for the survey.
Listen to Dr Dave Landrum from the Evangelical Alliance speaking to Premier's Des Busteed: