Lord Alton of Liverpool urged ministers to use the funding - which totalled £463 million last year - as leverage in helping ensure Asia Bibi can safely seek asylum in another country.
The crossbencher, who is a Christian, was quoted by the Daily Mail as saying a "failure" by the UK to "speak or act [on behalf of Ms Bibi] has been craven and shameful".
He also said: "Britain needs to do two things. First, give her sanctuary here.
"And second, until they uphold the rule of law and protect the country's minorities, we should redirect the £380,000 we give every day to Pakistan - £2.8 billion over the past two decades - to more worthy recipients."
Asia Bibi has been kept in a secret location in the Pakistani capital Islamabad for security reasons after she was acquitted of blasphemy last month.
Hard-line extremists, who accuse the mother-of-five of insulting Islam's prophet Muhammad, want her to be publicly hanged. She has always maintained her innocence.
Protests which erupted after she was cleared by the country's Supreme Court brought key roads in major cities to a standstill.
It is understood Asia is being prevented from traveling abroad until a petition calling for a review of the court's decision is heard.
Asia Bibi's husband, Ashiq Masih (pictured above with his daughter, Eisham) had called upon the UK, the US and Canada to offer asylum to her and the family.
On Wednesday, Theresa May says the UK was "close contact" with other countries to ensure the safety of Asia Bibi.
The Home Office has refused to comment on whether the UK is going to grant sanctuary to her in Britain.
Yesterday, the shadow foreign secretary Emily Thornberry accused ministers of "shameful cowardice" over a suggestion the UK has not offered asylum over fears the safety of British diplomats in Pakistan could be put at risk.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.