Revd Nadim Nassar, who also directs the Awareness Foundation which helps build relationships between Christians and other groups, made the comment as MPs held an emergency debate in Parliament over the number of refugees Britain should take in.
Prime Minister David Cameron said on Monday that the country would accept 20,000 Syrian refugees.
Mr Nassar said Britain was directly and partly responsible for the refugee crisis, because of its refusal to negotiate with the Syrian President Bashar al-Assad.
The British government has previously said it will not negotiate with al-Assad because of claims he used chemical weapons against his own people.
Revd Nassar agreed with the Conservative Christian MP Sir Gerald Howarth, who also told Premier it is necessary for Britain to work together with al-Assad in order to stop the refugee crisis completely earlier today.
However he strongly disagreed with Sir Howarth's opinion that Britain should prioritise taking in Christian refugees over other ones, calling the idea "total nonsense" and saying that Jesus Christ would never choose to help one equally needy person over another just because of their faith.
Nadim Nassar told Premier's News Hour: "Our government has blood on their hands... I challenge our government to prove me wrong. Where is the government's effort to help the Syrians end their conflict, instead of debating the refugees.
"Just thinking about 20,000 refugees until 2020, it suggests a horrific, horrific vision to the conflict in Syria. They are suggesting the conflict and the bloodshed will continue another five years, which means the whole world is absolutely sinking in shame.
"The whole world is not able to end one conflict after two world wars."
"If we ask Jesus Christ at the moment, 'would you like to prioritise your followers', what would he say? 'Yes, I would like to priotise the Christians'? This is total nonsense."
A civil war has been happening in Syria since 2011, between President al-Assad and government troops, versus a mixture of jihadist fighters like Islamic State and other secular rebel groups.
The United Nations says around 220,000 have died in the conflict, with more than 7.5 million people made homeless.
Listen to Premier's Des Busteed speak to Nadim Nassar here:
