Reverend Rose Hudson-Wilkin, who is also the Chaplain to the speaker of the House of Commons, said the current situation had given confidence to the underbelly that has always existed.
Speaking at the Church of England Foundation for Educational Leadership conference, she explained that despite having lived in the UK for decades she had never been racially attacked on the street until last year.
She said: "Whatever happens at the end of that (Brexit) it's about how are we going to keep the nation together.
"Over 30 years I have lived in this country. For the first time, last year, I was shouted at in the street and told to go back to Africa.
"Now I don't come from Africa, so I don't know which country in Africa they wanted me to go back to."
Jamaican-born Rev Hudson-Wilkin added: "So I think there has developed an unpleasantness, there's been an underbelly that has suddenly thought this is our time, we can do this and behave in this manner.
"So whatever happens, remember the vote was very close. Whatever happens at the end of March 29 it doesn't mean that people are going to say 'we've arrived now'.
"So we still need to be the ointment, we still need to be there praying and hoping and longing for the kind of unity that is going to see us down whatever pathway we go."
In her speech to the conference on Thursday Rev Hudson-Wilkin said many politicians would say that currently Parliament is a "rather bruising place to be".
"The verbal attack, the vile abuse targeted on them through the internet, and we know all too well that this can spill over into physical attack not just simply threatened, but real, as in the case of Jo Cox MP who was brutally murdered," she explained.
But she added that parliamentary democracy "is far too precious for us to give up".
However, Rev Hudson-Wilkin continued: "If we are going to be a truly resilient parliamentary democracy, then we are going to have to strongly resist the temptation of resorting to those defaults of behaviour that prevent us working together in a spirit of generosity and trust - the political point scoring, getting one up on the other, the football terrace shouting at one another.
"We need to regularly engage across the party and ideological divide."
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