In a open letter to the Times on Friday, they urge the British government not to recognise the upcoming Sudanese election, or the legitimacy of president Omar Al-Bashir.
Baroness Caroline Cox, a Christian and the founder and CEO of international aid agency Humanitarian Aid Relief Trust (HART), and one of a number of peers to have signed the letter, accused the government of idleness over the issue.
Speaking on Premier's News Hour, she said: "they're (Christians) being targeted and killed, churches are certainly targeted... Muslims and Christians are both being killed indiscriminately. It's genocide of Christians and genocide of black African peoples.
"These elections will be a kind of camouflage for legitimacy for a regime that deserves sanctions, not legitimacy.
"What I and other colleagues have recommended are targeted sanctions that wouldn't affect the people... [and] there needs to be proper, systematic, sponsored, humanitarian relief to help people.
"Pray for the people of Sudan, their suffering is indescribable. They desperately need your prayers."
President Omar Al-Bashir has led Sudan for more than 25 years, taking power in a military coup in 1989.
He was president for much of Sudan's second civil war, which started in 1983 and ended in 2005. During this civil war, two million people died, four million were displaced and hundreds of thousands were subject to human rights abuses such as slavery.
The International Criminal Court formally has also charged Omar Al-Bashir with genocide for his actions in Darfur, an area in western Sudan.
Omar Al-Bashir's presidency also saw the break-up of Sudan, with part of the country voting to become an independent country, South Sudan, in 2011.
Listen to Baroness Cox speaking to Premier's Aaron James: