Banking group, which has £8.5m slice of CSC, is under pressure along with other City investors from human rights charity

Lloyds Banking Group has become embroiled in a row over its investment in a company accused of involvement in the rendition of terror suspects on behalf of the CIA.

Lloyds, which is just under 40% owned by the taxpayer, is one of a number of leading City institutions under fire for investing in US giant Computer Sciences Corporation (CSC), which is accused of helping to organise covert US government flights of terror suspects to Guantánamo Bay and other clandestine "black sites" around the world.

Reprieve, the legal human rights charity run by the British lawyer Clive Stafford Smith, alleges that during the flights, suspects – some of whom were later proved innocent – were "stripped, dressed in a diaper and tracksuit, goggles and earphones, and had their hands and feet shackled". Once delivered to the clandestine locations, they were subjected to beatings and sleep deprivation and forced into stress positions, a report from the International Committee of the Red Cross says.

CSC, which is facing a backlash for allegedly botching its handling of a £3bn contract to upgrade the NHS IT system, has refused to comment on claims it was involved in rendition. It has also refused to sign a Reprieve pledge to "never knowingly facilitate torture" in the future. The claims about its involvement in rendition flights have not been confirmed.

Reprieve has written to CSC investors to ask them to put pressure on the company to take a public stand against torture.

Some of the City's biggest institutions, including Lloyds and insurer Aviva, have demanded that CSC immediately address allegations that it played a part in arranging extraordinary rendition flights.

Aviva, which holds a small stake in CSC via US tracker funds, said it had written to CSC's executives to demand an investigation. The insurer said it would take further action if it was confirmed that CSC was linked to torture. "Aviva is of course concerned by the allegations made against CSC," said a spokesman. "We are a signatory to the United Nations global compact, and support human rights principles, as outlined in the United Nations Universal Declaration of Human Rights. It is not yet clear that CSC is directly complicit in the activities outlined and we have written to the company seeking clarification. We will investigate these allegations further and take action as appropriate."

Lloyds said it was taking the allegations seriously and had launched its own investigation. A spokesman said: "Our policy is clear, we will not support companies whose ongoing business activities are illegal in the UK and breach the requirements of international conventions as ratified by the UK government. We are not aware of evidence that CSC is currently committed to activities inconsistent with our policy."

Lloyds holds an £8.5m stake in CSC via its Scottish Widows funds that track the S&P 500 index of America's biggest companies.

HSBC, another investor, said that it was not aware of evidence that CSC was breaching its ethical investment code.

CSC's alleged involvement with rendition came about after it purchased DynCorp, which was involved in hundreds of prisoner transfer flights, in 2003. While CSC went on to sell DynCorp in 2005, Reprieve alleges that CSC continued to be involved in the supervision of rendition flights until the end of 2006.

None of CSC's top 10 shareholders, including fund managers Dodge & Cox, Fidelity, Blackrock and Guggenheim Capital, a fund manager founded by a grandson of philanthropist Solomon Guggenheim, responded to the allegations made in a letter from Reprieve. Norway's sovereign wealth fund is also an investor.

One of the biggest investors, which declined to be identified due to its policy of refusing to comment on investment decisions, said its executives were "extremely concerned" about CSC's alleged links to torture, and managers raised their concerns with CSC as soon as it was made aware of the allegations by the Guardian.

Reprieve's legal director, Cori Crider, said: "CSC evidently thinks it's fine to profit from kidnap and torture as long as their shareholders are happy. It is now up to those shareholders, including British banks, pension funds and UK government [via Lloyds], to show this isn't the case. These institutions must insist that CSC take their ethical concerns seriously. Alternatively, they can vote with their feet."

Crider told investors that Reprieve had obtained an invoice indicating CSC organised a flight that took Khaled al-Masri, a German citizen mistakenly imprisoned by the CIA, from a secret detention centre in Afghanistan to Albania in May 2004. The charity said in its letter: "Having belatedly concluded after months of torture and interrogation that they had imprisoned the wrong man, the CIA, acting through CSC, arranged for Richmor Aviation jet N982RK to transfer Mr al-Masri from an Afghan 'black site' to a remote roadside in Albania."

In a letter to Reprieve, Helaine Elderkin, CSC's vice-president and senior deputy general counsel, said: "CSC's board of directors … have a corporate responsibility programme that fosters CSC's growth by promoting and increasing the value of the company to its shareholders, clients, communities and employees."

Lisa Nandy, the Labour MP who chairs the all-party parliamentary group on international corporate responsibility, also called on CSC's biggest investors to hold the company to account. "Investors have a unique responsibility to hold businesses accountable for their ethical conduct, particularly in relation to human rights. Corporates should conduct due diligence down their supply chains to protect human rights, working under the assumption that business should do no harm. Those that refuse to do so should have investment withdrawn," she said.

"The UK must take the lead in this area and ensure its institutional investors, many of which are using pension funds to allow grievous abuse, are asking tough questions at board level, demanding changes in behaviour and a corporate policy to uphold human rights."

CSC is being sued by some of its investors in relation to its £3bn contract to upgrade NHS computer systems.