Lord Leslie Griffiths, a Minister at Wesley's Chapel, told Premier he agreed with the Archbishop of York, Dr John Sentamu, who congratulated the council for its "fantabulous" idea.
Speaking during the News Hour, Lord Griffiths said: "The idea is a brilliant one. Westminster is a very wealthy city as well as a borough.
"Lots of people are paying the very highest council tax and I suppose that £800 or so extra per year can be absorbed into what they already pay."
Letters will be sent to homeowners in the highest council tax bracket - B and H - asking them to pay the voluntary tax.
Lord Griffiths said it was necessary for Westminster to address the issues vulnerable people face.
"It is a problem that shows itself in the city of Westminster almost more than anywhere else because those very expensive properties and all those shop doorways... there's nowhere where the world comes and is more aware of the social problem that we have, more profiled than Westminster," he said.
Asked whether he thought some residents would oppose the idea, he told Premier: "I think that whilst there is a resistance recognised by all policy makers about imposing extra taxes on people, I have a funny feeling that all of us have our consciences touched by seeing the huddled form of homeless people on the streets.
"We're all perplexed about it...and desperately want to give them something, and yet something holds us back, perhaps we're in a hurry, perhaps we wonder what they'd spend it on.
"I just wonder if there were a hypothecated tax - that is a tax which if you paid it, we know would go towards alleviating the plight of such people, I have a funny feeling that everyone would want to do something... even though they find it difficult to know what to do when they see someone homeless on the streets."
While he added that he would be encouraging church members to make the voluntary payment, he also said he would practise what he preached.
"I'll pledge some of my income towards it because I'd be glad to think I can do something instead of feeling so helplessly at sea at the moment not knowing what to do," he said.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.