The head of Britain's race relations watchdog yesterday backed Jack Straw's request for Muslim women to remove their veils during personal encounters.
Trevor Phillips' intervention came as Higher Education Minister Bill Rammell also weighed into the debate by supporting universities that banned the full-face veil.
Mr Phillips, chairman of the Commission for Racial Equality, said Mr Straw was right to raise the issue if it made him feel uncomfortable.
But he added that there was no justification for telling people what to wear, insisting that any concerns about the veil were "a matter of negotiation".
Gordon Brown last night backed Mr Straw, agreeing it would be "better for Britain" if fewer women wore veils.
The Chancellor's comments followed the Commons Leader's virtual isolation by the rest of the Cabinet and a storm of protest from many Muslims.
Mr Phillips told MPs today: "I think it is perfectly reasonable for him to say he feels uncomfortable about it.
"I think it is right for him to say 'would you mind not making me feel uncomfortable' in this case, as long as it is clearly understood that the answer to that can be 'no'."
But Mr Phillips also told the Commons Education Select Committee there was a need to separate the convenience of public situations from social conventions.
Mr Rammell yesterday praised Imperial College's recent decision .
"I'm not dictating hard and fast rules, but Imperial College recently banned the face veil and I think that this is arguably the best decision."