Two Tory councillors have quit the party in protest after a council leader called for rough sleepers to be cleared before the royal wedding in May.
Simon Dudley, leader of the Royal Borough of Windsor & Maidenhead, had said beggars could show Windsor in an "unfavourable light" when Prince Harry weds Meghan Markle.
He won a no-confidence vote on Monday.
Paul Brimacombe and Asghar Majeed immediately resigned from the council's Conservative group.
The pair will continue as independents.
They said in a joint statement: "It was not considered appropriate… to wholeheartedly disagree with the will of the group on this fundamental issue and yet to remain within the group."
Mr Dudley made his initial remarks about tackling "aggressive begging" in a letter to the local Police and Crime Commissioner (PCC) but has since claimed his comments were misconstrued.
The leader of the Conservative-controlled authority said he was referring to anti-social behaviour not homelessness.
Mr Dudley survived a no-confidence vote held by the council's Conservative group.
It is expected the opposition group within the council will attempt to oust him with a no-confidence vote on January 29.
"At no point have I said 'move on the homeless'," Mr Dudley told the BBC, before apologising if he was not "clear enough in my communication".
The prime minister is among those who disagreed with Mr Dudley's views, saying that councils "should work with police" to ensure accommodation is provided for homeless people.