Rt Revd Nick Baines and Ephraim Mirvis were speaking after a number of predominantly Muslim countries made or repeated bans on the public celebrations of Christmas this year.
The Sultan of Brunei said anyone publically celebrating the birth of Jesus faced up to five years in prison, or a fine of up to $20,000.
Hassanal Bolkiah said the ban was to protect the country's population, and that non-Muslims could celebrate Christmas privately as long as they notified the government.
And Somalia also reiterated a 2013 ban on Christmas celebrations, with its Religious Affairs minister Sheikh Mohamed Khayrow saying that they are "contrary to Islamic culture".
The persecution of Christians has hit the headlines a number of times in recent years.
Islamic State has killed thousands of Christians as well as Muslims and Yazidis, predominantly in the Middle East.
The Islamist groups Boko Haram and al Shabaab have also killed Christians and people of other faiths in Western and Eastern Africa.
And Chinese authorities have removed hundreds of churches crosses and completely demolished other churches in the country.
It is illegal to be a Christian outside of state-sanctioned churches in China, forcing many Christians to worship in house or underground churches.
Rt Revd Nick Baines (pictured above) wrote in The Times: "We are talking about men, women and children being singled out because of their Christian faith or identity and put to an unimaginably cruel death.
"Or being driven out of home, away from livelihood, deprived of identity and dignity.
"Or, for women and girls, being forced into sexual slavery and subjected to rape-at-will.
"When my Christian brothers and sisters suffer... they rely on the rest of us to tell their story and to use what powers we have to bring political pressure for an end to such suffering."
And Ephraim Mirvis told the paper: "Faith communities have a responsibility to stand together to oppose discrimination.
"The shocking ban on public celebrations of Christmas in Brunei is reflective of an intolerance that, as Jews, we simply cannot countenance."