The BHA was forced to change its original campaign slogan 'If you’re not religious, for God’s sake say so’, after the Committee of Advertising Practice advised that it could cause "widespread" and "serious" offence.
The campaign is targetted at people who might tick the 'Christian' box in answer to the question 'What is your religion?', even though they are not practising Christians and would not normally go to church.
The BHA argues that the results of the last census in 2001 gave a distorted picture of the religious composition of Britain and that there is a need for greater accuracy.
Theos said that the BHA's campaign failed to acknowledge that, as with the previous census, the religious question is the only optional question on the form, and that ‘No religion’ is the first option available to respondents in the list of possible answers.
The think tank said people had "ample opportunity" to deny any religious affiliation if they wanted to, and that humanist claims that respondents are “funnelled… into giving a religious response” are "simply untrue".
Commenting on the campaign, Paul Bickley, Senior Researcher at Theos said the humanists were doing a good job of keeping religion in the news but added that there was "clearly a mistake" with this campaign.
“The campaign grossly exaggerates the extent to which the religious affiliation results of the 2001 census have shaped government policy or influenced spending decisions," he said.
“In any case, the British people are quite capable of judging for themselves what box they should tick. They don’t need to be told.
“If the Archbishop of Canterbury were to launch a campaign pleading for people to tick the Christian box, it would be rightly ridiculed as a sign of desperation.
"I suspect that this is what may happen with this campaign, too."