Lord Alton has challenged the UK Government to put more pressure on Pakistan to stop the persecution of Christians and other religious minorities.
Lords heard how religious minorities in the Muslim-majority country are being "ghettoised into squalid colonies" and subjected to "shocking" levels of persecution.
Lord Alton contrasted this with the vision of Pakistan's founding father, Muhammad Ali Jinnah, of a nation where minorities would be welcome - a vision that the Pakistani government remarkably endorsed even while coming under intense pressure over the treatment of Asia Bibi, a Christian woman freed from death row for blasphemy last year.
"My Lords, Pakistan's illustrious and enlightened founder, Muhammad Ali Jinnah, crafted a constitution which promised to uphold plurality," he said.
"Tragically, 70 years later, Pakistan's Ahmadis, Christians, Hindus and minorities, such as the last 4,000 remaining Kalash clinging to a precarious existence in three remote valleys, all face shocking persecution and discrimination."
He refuted the Pakistan Foreign Minister's recent claim that individual incidents of persecution were being whipped up by "western interests", saying that the country "fails the Jinnah test" on religious liberty.
"Pakistan fails the Jinnah test, not western interests, when no one is brought to justice for the murder of the Christian Minister for Minorities, Shahbaz Bhatti," he said.
"It fails the Jinnah test when 1,000 Hindu and Christian girls are forcibly married and converted. It fails when, in Punjab, Sadaf Masih, a 13 year-old girl, is kidnapped, forcibly converted and married and when, in Sindh, the same thing happened to two Hindu girls."
He asked the Government what assessment they had made of the relationship between their aid programmes and human rights, and the treatment of minorities in Pakistan, and in particular the case of Mrs Bibi.
"Over the past decade, £2.6 billion of British aid has poured into Pakistan—on average, that is £383,000 every single day—but failure to differentiate how and where we spend that money leads DfID [the Department for International Development] to say that it has no idea how much of the aid reaches these destitute, desperate minorities," he said, noting a recent report from the National Audit Office, which said that "overall Government is not in a position to be confident that the portfolio in its totality is securing value for money".
He called on DfID ministers to reassess how UK money is spent and "why it does not target beleaguered minorities and why it is not made conditional on the removal of hate material from school textbooks and discriminatory adverts reserving menial jobs for minorities".
"I hope they will insist that the provision of an affirmative action programme, endorsed by the constitution, is implemented," he said.
He urged the Government to make representations to Pakistan about its controversial blasphemy laws, which are often misused against religious minorities and even some Muslims for personal gain or score settling.
He also expressed his desire to see Prince William and the Duchess of Cambridge meet with religious minorities and visit the colonies where they live during their visit to Pakistan later this year.
During the debate, the Bishop of Coventry, the Rt Rev Christopher Cocksworth, said there had been a "strong case" for the UK to offer asylum to Mrs Bibi.
The UK came under fire after it failed to offer the Christian mother-of-five asylum. She instead went with her family to Canada.
"I am troubled by how parliamentarians can hold the Government to account in cases such as this when we are told that live cases are not open to discussion," he said.
"That sense of dis-ease is reinforced by the absence of evidence of diplomatic activity in the Asia Bibi case before it became an international news story," he said, adding that he was "not yet persuaded" that the mechanisms were in place in DfID to ensure that UK aid was going to the places it was needed, including Pakistan's minority community.
Responding to the concerns raised during the debate, international development minister Baroness Sugg said that freedom of religious belief was a "high priority" for the Government's work in Pakistan.
"We raise it regularly at the highest levels of government and support grassroots campaigning with our programmes," she said.
She said that the Government was "deeply concerned" by the misuse of blasphemy laws and that its long-term objective was to "overturn" them.
Addressing concerns around DfID spending, she said the Government was working with NGOs to target aid at minorities but admitted it needed to "do more" to ensure they were being reached.
"I reassure [Lords] that our development assistance really targets the poor, regardless of race, religion, social background or nationality," she said.
"We know that those affected by discrimination are likely to be among the poorest. We know, and our NGO partners have confirmed, that our focus on the poorest and most marginalised ensures that we benefit minority groups."