Trevor Phillips, chairman of the Commission for Racial Equality, said the divisions exposed in the debate that his dominated British media for more than two weeks risked sparking "fire" on the streets.
He said the friction between communities risked becoming "the trigger for the grim spiral that produced riots in the north of England five years ago. Only this time the conflict could be much worse".
"All the recent evidence shows that we are, as a society, becoming more socially polarised by race and faith," Phillips wrote in The Sunday Times newspaper.
"The only place where this may not be true is in our schools and the main reason is that in many of our cities things cannot get any worse."
He called for a "civilised" debate on race.
The veil has been at the centre of a political storm over Muslim integration, with Prime Minister Tony Blair entering the debate by calling the veil a "mark of separation".
Jack Straw, the leader of parliament's House of Commons and a former foreign secretary, sparked renewed debate when he disclosed that he asked Muslim women to remove their veils when they came to consult him in his constituency.
Straw represents the industrial northwestern English town of Blackburn, which has a large Muslim minority of South Asian origin.
Phillips criticised Muslims who had lambasted Straw.
"The so-called Muslim leaders who initially attacked Straw were wrong," he wrote.
"They were overly defensive and need to accept that in a diverse society we should be free to make polite requests of this kind."
He warned the veil debate was becoming dangerously polarised.
"On one side of the trenches we have those who want a fully fledged auto-da-fe (burning of a heretic) against British Muslims in which anything any Muslim does or says must be condemned as a signal of their wilful alienation and separation.
"On the other hand the defensiveness of some in the Muslim communities has hardened into a sensitivity that turns the most neutral of comments into yet another act of persecution.
"This is not what anyone intended and it is the last thing Britain needs."

Copyright AFP (Agence France-Presse), 2006